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18 Episodes 1985 - 1986
Episode 1
Tue, Sep 24, 198560 mins
When David's brother Richard shows up, he does not only seem to be a rich man, but also makes an impression on Maddie. While David has got to handle his jealousy, Maddie has trouble to pay back her $37 000 debt to the bank. When David is attacked by a stranger, who wants back his money, David realizes that all the money that his brother spends does not belong to him.

Episode 2
Tue, Oct 1, 198545 mins
A mysterious woman appears in Maddie's and David's agency, who does not want to show her face. She wants Maddie and David to find her former lover, who is the reason why she can't show her face. The two detectives find this man, but find out on the next day that someone murdered him. Of course, the mysterious woman is their very first suspect.

Episode 3
Tue, Oct 8, 198547 mins
Maddie learns where the accountant who took her money is and is determined to get it back, David tries to talk some sense into her, telling her he is in South America so her money is gone. She won't listen and hopes a plane, she imagines him feeling guilty and apologizing instead he maneuvers he out, and just when she thinks all hope is lost David shows up. With him they win, but if they won some other poor sucker lost, Maddie want's him to be the poor sucker. They get him in a little one on one, $100,000 to start Maddie puts up her house and car. When it comes to the moment of truth will she give up her night's winnings and walk away with her house, car, and dignity, or will she risk it all.

Episode 4
Tue, Oct 15, 198550 mins
After meeting with a client in an old nightclub, David and Maddie learn about a murder that took place there: the singer and a cornet player fell in love and killed her husband. They went to the chair saying the other one did it. David and Maddie discuss the murder: David thinks the woman did it, Maddie thinks the guy did; they wind up insulting each other. At home they each have a dream (in black and white) recapping what happened in 1946. Maddie dreams of the singer and her husband who've remained friends though the fire has gone out of their relationship; the cornet player arrives and seduces her, convincing her to get rid of the husband. He kills him, making it look like an accident, but then tells the cops she did it. David's version has the new cornet player coming to the club just wanting to play; she has a bad marriage and he was her way out; she seduces him, gets him to kill her husband, then sends him off to fry.

Episode 5
Tue, Oct 29, 198550 mins
After Maddie walks in on a limbo contest in the office, she bets David he can't behave like a mature adult for a week. They get a client, a woman whose stepson has been kidnapped and wants to negotiate for the best deal. When they go to drop off the money, they find her son is his own kidnapper. Maddie and David agree not to tell the mother but are shocked when he is taken again the very next day. The effort to act soberly takes its toll on David, changes the office atmosphere for the worse, and Maddie longs for the old David.

Episode 6
Tue, Nov 12, 198549 mins
Maddie is hired to find a silver locket by an old girlfriend of David's. He has strong feelings for her and thinks that her husband is trying to kill her. However, Maddie isn't so sure, especially when she kills her husband in self-defense.
Episode 7
Tue, Nov 19, 198548 mins
An Irish girl who claims to be a leprechaun wants to hire the Blue moon detective agency to protect her. David is willing to take the case, but Maddie thinks that the girl is mentally ill and needs a psychiatrist, not a detective agency.

Episode 8
Tue, Nov 26, 198548 mins
The agency has finally made a profit and so David and Maddie have disagreement over how to spend it. An artist, whom Maddie has never met, paints a picture of her and then shoots himself. Maddie decides to spend the agency's profit on purchasing the portrait. When the artist's brother turns up to see the portrait, Maddie decides to give him the portrait. He is also killed but it turns out that he is an international art thief. It all appears to be part of a conspiracy to steal a valuable painting called 'The Duchess'.
Episode 9
Tue, Dec 10, 198549 mins
A rival detective agency has made an offer for Blue Moon Detective Agency and Maddie is seriously considering accepting the offer. Addison is upset and storms out and heads to a bar. Whilst there, he meets a man about to be sacked because his Rolodex of celebrity phone numbers has been stolen. Addison decides to help the man find his property. However, Maddie decides to sell the agency and so Addison decides to set up his own agency. Nothing works out well so Maddie decides to ask for her agency back again.

Episode 10
Tue, Dec 17, 198560 mins
It's Christmas time and Addison has set up a Santa hot line in the agency to earn some money. At the same time, a criminal in the witness protection scheme is killed but his wife and baby who witnessed the murder manage to escape. When fleeing, the baby is left in Agnes' apartment but without any explanation. Maddie and Addison decide to try to find the mother. The mother eventually turns up at the Blue Moon agency looking for Agnes and her baby.

Episode 11
Tue, Jan 14, 198650 mins
It's a missing person case. Alan Tupperman wants to get married and he knows to who, he has a full description of his perfect woman, he's just never met her and hires the agency to find her. David and Maddie have different interpretations of his list and hold a contest over who will find his bride. Maddie's choice is all about substance, David's is all about looks. They send over both girls and let him decide. When looking for an answer they find he may have married both of them, investigating further only leads to more things that don't add up.

Episode 12
Tue, Jan 21, 198649 mins
Agnes is feeling down and feels that her life is in a rut. To cheer her up, Maddie and Addison decide to send her to the annual California Investigator's Association Ball. Maddie does a makeover on her and she goes the ball and meets a man, who appears interested in her. The next day she meets him at a bowling alley where he is stabbed, but then his body disappears. That is just the start of her problems.
Episode 13
Tue, Feb 11, 198646 mins
Its Maddie's birthday but she is underwhelmed at the thought. An escape artist is drowned when he fails to exit his trick water cabinet. His widow approaches the Blue Moon agency asking for protection. Her husband had threatened her with revenge for a prior indiscretion and she wants his body watched until it is cremated. The body disappears, which means Maddie and Addison have to find him before he carries out his threats.
Episode 14
Tue, Feb 18, 198644 mins
Maddie's parents are in town for a wedding. However, her mother is worried that her father is having an affair. Maddie decides to follow her father to prove that he is not having an affair. To spare her possible embarrassment, Addison decides to do it for her.

Episode 15
Tue, Mar 11, 198648 mins
A dying man comes into the agency stating that he is going to be murdered. He has an incurable disease but wants the insurance payout for his family. He offers Maddie and Addison $25 000 to be a witness. Maddie doesn't want anything to do with it but Addison wants to do it. When he arrives, the man is dead and Addison thinks he did it, so he goes on the run with the police after him.
Episode 16
Tue, Apr 1, 198648 mins
David gets tips from a prostitute (Toby) with a client named Jerry who talks in his sleep. It happens that Jerry is connected with organized crime, and talks about murders and other crimes that are about to happen. David and Toby make a deal about sharing the information and getting the award money from every case which Jerry talks about in his sleep. David becomes a very famous detective who solves murder cases. The whole thing works wonderfully for David; he has Maddie believing that he's the best detective in the world; until Jerry tells Toby that David is the next one to be murdered.

Episode 17
Tue, Apr 29, 198648 mins
Maddie invites Addison to a family wedding to stop being introduced to all the single men. Addison is delighted to attend but Maddie is not happy about his enthusiasm. So she decides to pay him to be her escort. A man's wife is killed in a car accident, which leaves him so upset he wants to die. He arranges to have himself killed by a hit man after three days. Then, from his office, he sees his wife in the street but by the time he gets down there she has gone. He then hires Blue Moon Investigations to stop the hit, which they do. They are then hired to look for his wife, but not before he is still killed. However, at least their investigation stops them have to go to the wedding.
Episode 18
Tue, May 13, 198649 mins
Camille is a con woman and is about to marry an elderly man when he suddenly dies. Then she is arrested by a crooked detective. When she escapes from his custody, she accidentally stops an assassin killing an American senator. Addison has the bright idea of employing Camille at Blue Moon Investigations to raise the profile of the company. When she is hustled by the crooked cop, she decides to join Blue Moon Investigations. However, things don't work out as she is unable to get away from her past.