Aging illusionist Wendell Muse is hassled by authorities when a series of suspicious fires plagues his performances. Muse hires the Angels to prove that he is not moonlighting as an arsonist.

A jilted gigolo murders a wealthy woman and pins the crime on a jewel thief. Charlie calls in the Angels to set a trap. Kelly poses as a lonely heiress, Kris plays a Swedish movie star, Bosley a flamboyant auctioneer and Sabrina a hotel employee.

In hopes of contacting her beloved nephew Martin who died four years ago, Claire Ross sponsors Dr. Douglas Holden and his psychic research. Bosley, Claire's friend, brings in the Angels as fake psychics to check on possible fraud.

A young woman is murdered after she identifies a killer on a luxury liner. The Angels are called in to uncover a ring that helps criminals escape the country by cruise ship.

Ex-mobster Jake Garfield has just been released from prison for the murder of his wife. He claims that he was framed by a racketeer named Renaldi, so his nephew hires the Angels to investigate.

The Angels act upon a mysterious telephone call from Charlie to come to an island in Mexico. When they arrive the boatman leaves taking their baggage and weapons, and the threesome are stranded on the beach.

When three unsuspecting investors are taken by racketeer Harley Dexter, the Angels scheme to con Dexter into returning the money.