A key question in the lawsuits is whether Aereo's technology provides users with a "public performance" of the plaintiffs' content. Copyright owners have the exclusive right to public performance of their works.
Fox, CBS and NBC broadcast both NFL and MLB games. The sports leagues argued that Aereo is illegally rebroadcasting signals without licensing the content for which it charges other companies such as Verizon and DirecTV hundreds of millions.
"This judicially created loophole allows such services to avoid the force of the Leagues' copyrights in broadcasts of their games, eroding the value of one of the Leagues' most important assets," the leagues said about Aereo.
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The leagues said they will be left with no choice but to move their games to cable TV networks, which Aereo cannot carry for free.
"The option for copyright holders will be to move that content to paid cable networks (such as ESPN and TNT) where Aereo-like services cannot hijack and exploit their programming without authorization," the leagues said.
A spokeswoman for Aereo declined to comment on the filing.
Some top-tier sporting events have already migrated to cable, such as some of the games in the NCAA Men's basketball tournament, which airs on some Turner-owned networks, and some baseball playoff games.
The leagues said about 90 percent of their regular-season games are on broadcast TV, which also feature all NFL playoff games and the heavily viewed Super Bowl.
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Major League Baseball allows broadcasters to air about 400 games per year, including the World Series on Fox.
The leagues said Aereo also threatened its sports packages that offer out-of-market games to fans—"an important source of income."
One of the NFL's concerns expressed in the filing was that Aereo could create a service similar to NFL Sunday Ticket, which is DirecTV's exclusive package of out-of-market football games on Sundays.
DirecTV pays the NFL an estimated $1 billion per year for the rights to offer the games to its subscribers and is currently in an exclusive negotiating window with the league to renew the deal.
Major League Baseball also has an "MLB Extra Innings" package that pay-TV subscribers can buy, as well as an Internet service.