Hashim Rahman Jr., 23, and younger brother Sharif Rahman, 18, accuse Showtime Networks and Mayweather of profiting at their expense.
The lawsuit filed last week in Nevada state court seeks unspecified monetary damages of more than $10,000 from the New York-based network and Mayweather, who goes by the nickname "Money."
Mayweather's attorney, Mark Tratos, declined to comment. Showtime officials didn't immediately respond to a message.
The lawsuit also accuses Mayweather of lying in testimony Sept. 23 before the Nevada State Athletic Commission about the "All Access" show at his gym.
"Defendant Mayweather falsely testified that Hasim's 31-minute fight did not happen as aired, and that the fighters took several breaks," the document said.
The lawsuit alleges that Mayweather forced Sharif Rahman to fight several rounds lasting five to seven minutes in length and said that if Rahman left the ring, he faced beating by others.
"Sharif feared for his safety and was forced to fight," the lawsuit said.
The lawsuit also says Sharif Rahman didn't sign a release agreeing to be filmed or having his name used for the show and that Hasim Rahman Jr. fought the same boxer for more than 30 minutes with no breaks.
The Rahman brothers are the sons of former professional heavyweight boxer Hasim Rahman Sr.
Their attorney, Vicki Greco, declined comment about the lawsuit filed Thursday in Clark County District Court.
Mayweather was licensed this year as a promoter in Nevada. His attorney, Shane Emerick, told the athletic commission last month that Mayweather knows that gambling in the gym is illegal and scenes showing cash exchanging hands in bets on the fighting didn't really happen.
The boxer and his attorney also discussed the appearance of marijuana on the show. They said that despite "All Access" showing Mayweather at his Las Vegas mansion while marijuana cigarettes are rolled and smoked, Mayweather doesn't smoke the drug or drink alcohol and wouldn't be around secondhand pot smoke because it could show up in drug tests.
Asked Monday whether commissioners were satisfied with Mayweather's responses, commission Chairman Francisco Aguilar referred questions to Bob Bennett, commission executive director.
Bennett said the commission wasn't a party to the lawsuit and declined to comment Tuesday.