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O.A.D. December 3, 1977 . "Dear Beverly; The Strike; Special Delivery" . Advice columnist Beverly Blanchard (Eva Gabor) neglects her husband, Russ (Leslie Nielsen), who thus spends time with a fellow passenger (Stephanie Blackmore). Captain Stubing wages war with a visiting chef, Antonio Borga (Al Molinaro). Julie's friend, Jeff Smith (Robert Urich), is separated from his wife, Gail (Pamela Franklin), but doesn't know that she's on board and carrying his child. Guest Stars: Pamela Franklin as Gail Smith, Eva Gabor as Beverly Blanchard, Al Molinaro as Chef Antonio Borga, Leslie Nielsen as Russ Blanchard, and Robert Urich as Jeff Smith (credited as Bob Urich). Other Guests: Meg Wyllie as Sister #1, Mary Treen as Sister #2.

O.A.D. November 26, 1977 . "Romance Roulette; The Captain's Captain; Dog's Life" . Three women (Jane Curtin, Susan Heldfond, Joanna Kerns) romance—but complications occur when they try to dump three men. The Captain's father (Phil Silvers) visits and falls for a galley cook (Judy Canova). A security dog traps a passenger (Gary Burghoff) in his bathroom. Guest Stars: Gary Burghoff as Donald M. Flanders, Judy Canova as P. J. Muldoon, Jane Curtin as Regina Parker, and Phil Silvers as Merrill Stubing, Sr. ('Stubby'). Other Guests: David Landsberg as Morton, Vincent Baggetta as Frank Vallone the plumber (credited as Vince Baggetta), Joanna Kerns as Beth Luckner, and Susan Heldfond as Toby Chapman. Others: Peter Mensah as Passenger (uncredited).

O.A.D. November 19, 1977 . The Understudy; Married Singles; Lost & Found . A cruise-director trainee (Jo Ann Harris) is after Julie's job. A bickering married couple (Polly Bergen, Steve Allen) pose as swinging singles. A childless couple (Sandy Duncan, Jim Stafford) takes in a young runaway (James Bond III). Guest Stars: Steve Allen as Durwood Moss, Polly Bergen as Maisie Nolan, Sandy Duncan as Sharon Baker, Jo Ann Harris as Connie Evans, and Jim Stafford as Richard Baker. Other Guests: Loni Anderson as Barbie, Joshua Bryant as Jack Plymouth (credited as Josh Bryant), J. Jay Saunders as Mr. Dennison, Marilyn Coleman as Mrs. Dennison, Hayden Rorke as Mr. Humbertson, and James Bond III as Theodore Dennison, Jr.

O.A.D. November 12, 1977 . "Identical Problem; Julie's Old Flame; The Jinx" . Identical twins (Diana Canova in a dual role) bewilder a smitten Doc. Julie tries to dodge a former beau (David Hedison). The crew blames a "jinxed" couple (Ray Bolger, Harriet Nelson) for a series of accidents. Guest Stars: Ray Bolger as Horace McDonald, Harriet Nelson as Henrietta McDonald, Diana Canova as Ellen Edwards / Helen Edwards, and David Hedison as Buddy Stanfield. Other Guests: Alana Stewart as Mrs. Stanfield (credited as Alana Collins).

O.A.D. October 29, 1977 . "Joker Is Wild; First Time Out; Take My Granddaughter, Please" . Has-been comic Barry Keys (Phil Foster) asks Julie to let him entertain on board to return a favor. Mrs. Warner (Ruth Gordon) is determined to marry off her granddaughter Shirley (Patty Duke). College pals bet on whether virginal Dan (Robert Hegyes) changes his status before the cruise ends. Guest Stars: Patty Duke as Shirley Warner (credited as Patty Duke Astin), Phil Foster as Barry Keys, Ruth Gordon as Mrs. Warner, Robert Hegyes as Danny, Tab Hunter as Dave King, Maureen McCormick as Barbara Holmes, and John Mark Robinson as Lee. Other Guests: W.K. Stratton as Kyle, Meegan King as Paul, and Robert Hackman as Freddy Stevens – Booking Agent (credited as Bob Hackman).

O.A.D. October 22, 1977 . "Help! Murder!; Isaac The Groupie; Mr Popularity" . Isaac's favorite singer, Roxy Blue (Diahann Carroll), becomes his lover. Talky Robert Tanner's (Jim Nabors) popularity increases when fellow passengers think he may be a jewel thief. Bert Fredericks (David Groh) plans his wife Denise's (Michele Lee) birthday party, but she thinks it's a murder plot. Guest Stars: Diahann Carroll as Roxy Blue, David Gro as Bert Fredericks, Michele Lee as Denise Fredericks, Jim Nabors as Robert Tanner (later claims to be 'Roscoe Toller'), and Reva Rose as Myra Grove. Other Guests: Olan Soule as Harvey Grove (credited as Olan Soulé), and Robert Hastings as Customer (credited as Bob Hastings).

O.A.D. February 11, 1986 . "In God We Strongly Suspect" . David and Maddie are hired to watch over the body of an escape artist. He threatened that he would come back from the dead and kill his widow. The detectives spend the night in the morgue, but in the morning the corpse has disappeared, and soon afterwards the widow is found dead. Maddie and David discover that the escape artist is in fact still alive and involved in a diamond heist, during which he seemingly dies again.

O.A.D. January 21, 1986 . "North by North DiPesto" . Agnes is looking for some excitement in her life, so Maddie and David give her their tickets to a top industry banquet. This leads to her involvement in an espionage operation which sees her kidnapped and interrogated. She manages to escape to a laundry, and discovers that it is being used by spies to hide stolen plans. Her adventures lead her to conclude that she is happy with her life after all.

O.A.D. January 14, 1986 . "The Bride of Tupperman" . A wealthy but lonely man hires the detectives to find him a suitable wife. Although Maddie initially does not want to take the case as Blue Moon is not a dating agency, they eventually decide to go their separate ways, each finding a candidate based on their own ideals. The client seems to choose the woman selected by David, but then it transpires that not only did he choose both women, but that he was already married. When they attempt to confront him, they find the woman chosen by David dead and the client in the hospital, which leads them to discover his true scheme.

O.A.D. December 17, 1985 . "Twas the Episode Before Christmas" . A man named Joseph is murdered by criminals he testified against and his wife, Mary, leaves her baby in Agnes' apartment. She enlists Maddie and David to help find the baby, and encounters "the three kings" (three FBI agents all called King). The baby's mother eventually turns up at Blue Moon, but Agnes and the baby are gone, and are eventually found at Maddie's house being held at gunpoint. The episode ends with the cast, crew, and their families singing a Christmas carol to the viewers.

O.A.D. December 10, 1985 . "Atlas Belched" . David takes a case from a young executive (Mark Linn-Baker), who has lost his boss's prized Rolodex containing the contact details of a number of celebrities. When the detectives assist him in tracking it down, he attempts to hold it hostage. Meanwhile, Maddie sells the agency to a wealthier rival firm, which upsets David, who announces his intention to start up his own agency. Maddie realizes she has made a mistake and convinces her rival to give the agency back to her.

O.A.D. November 1, 1986 . "Who's the Boss?" . Jamie has a dream that he's the boss of his parents.

O.A.D. November 12, 1985 . "Knowing Her" . Maddie takes a wealthy female client (Dana Delany) who wants to retrieve a stolen locket. David, who used to date the client, begins to suspect that her estranged husband is threatening her when she has a series of apparent accidents. The client shoots her husband during a confrontation and it looks like self-defense, but Maddie is not convinced.

O.A.D. October 29, 1985 . "My Fair David" . After walking in on an office limbo party, Maddie bets David that he will not be able to act like a mature adult for one week. If he loses, he must fire two employees, whereas if she loses she must limbo in front of all the staff. David loses the bet, but Maddie lets him off the hook. The duo are also involved in a case surrounding the kidnapping of a concert pianist. Moonlighting was preempted by the third game of the 1985 World Series on October 22, 1985.

O.A.D. October 1, 1985 . "The Lady in the Iron Mask" . David and Maddie are hired by a woman in a veil to track down an ex-boyfriend who threw acid on her face in a fit of anger. She claims she wants to give him another chance, but shortly after they find him, he is killed. The investigators discover that the person who actually hired them was an impostor and must find the real killer, leading to a chaotic chase scene in which everyone is wearing the same dress and veil.

O.A.D. Mar 3, 1985 . Pilot (Episodes 1 & 2) . Maddie Hayes wakes up to find her staff have quit and all her money has been stolen. One of her few remaining assets is a loss-making investigation agency run by David Addison. She sacks the staff but David is determined to keep it going.

O.A.D. March 5, 1985 . "Gunfight at the So-So Corral" . Maddie arrives for her first day of work at the renamed Blue Moon agency to find there are no cases on the books, so David poaches one from a rival agency. The detectives set out to find their client's missing son, but find out that he is a contract killer. Unbeknownst to them, their client (Pat Corley) is also a hired killer and they are caught in the middle as the two men meet for a shoot-out. Tim Robbins also appears in this episode.

O.A.D. November 19, 1985 . "Somewhere Under the Rainbow" . A woman is being chased by several men, and hires the agency to protect her. She claims to be a leprechaun and that the men are after her pot of gold. Maddie does not want to take the case, as she believes the woman needs psychiatric help, but David gets her involved anyway. The "pot of gold" turns out to be loot stolen from a bank in Ireland by the woman's father many years earlier.

O.A.D. October 4, 1986 . "Here Comes the Judge" . Jamie plays a judge in his school's mock courtroom.

O.A.D. September 27, 1986 . "My Mother the Teacher" . When Jamie's teacher is ill, Joan Lawson gets hired as a substitute. She lets Jamie, Vicki and all Jamie's friends know there will be no favoritism nor nepotism in her classroom.

September 20, 1986 . "Money, Money, Money" . Jamie thinks that his crush Jessica will only like him if he has a lot of money.

O.A.D. September 13, 1986 . "Chewed Out" . Jamie and Reggie try smoking for the first time in an effort to be mature. Vicki tries smoking too, which angers Ted. Adam Rich guest stars.

O.A.D. May 17, 1986 . "The Grandparents" . Ted reveals to his visiting parents that Vicki is a robot.

O.A.D. May 3, 1986 . "Show Biz (a.k.a. Vaudeville Vicki)" . A vaudeville actor (Ken Berry) becomes convinced that Vicki is his long-lost daughter.

O.A.D. February 22, 1986 . "Good Ol' Lou . Ted is motivated to get the family into shape when an obese coworker loses a record amount of weight.