In the year 2071, the crew (Spike, Jet, Faye, Ed, and the Welsh Corgi named Ein) of the spaceship Bebop travel the solar system bringing bad guys to justice and trying to make some cash while doing it. In the slang of the era, "Cowboys" are bounty hunters. Most episodes revolve around a specific bounty, but the show often shares its focus with the pasts of one of each of the four main characters.

Set in the 1920s, two decades after the first series ends, the plot follows the courtship of two teenage Forsyte cousins: Fleur and Jon. Fleur, the daughter of Soames and Annette, and Jon, the son of Irene and Jolyon, meet by chance as youngsters; now Irene's son has fallen in love with the daughter of Soames, the man she despises above all others. Fleur and Jon haven't a clue that Soames and Irene were once married, all they know is that the family...