The men who run America's professional sports leagues wrung their hands before a congressional committee yesterday and warned that federal legislation is the only cure for the "chaos" and "turmoil" currently afflicting their billion-dollar games.

"The basic need is for the elimination of confusions and risks -- to communities, fans, and leagues -- that recent court rulings have created," Pete Rozelle, National Football League commissioner, told the Senate Committee on Commerce, Science and Transportation, which is considering two bills designed to give sports leagues the right to control the location of their franchises.

That right has been eroded in the past five years by legal rulings, particularly the $49 million antitrust judgment against the NFL for trying to block the unauthorized move of the Oakland Raiders to Los Angeles. Since that ruling, the NFL's Baltimore Colts moved to Indianapolis and the National Basketball Association's San Diego Clippers relocated to Los Angeles, both against the wishes of their leagues. Other teams in both leagues have announced their intentions to follow suit.

Rozelle, along with David Stern, commissioner of the NBA; John Ziegler, president of the National Hockey League; Alexander Hadden, major league baseball's deputy commissioner; Harry Usher, commissioner of the U.S. Football League, and Earl Foreman, commissioner of the Major Indoor Soccer League, took turns asking the committee to restore to their leagues the legal right to control "the game of musical chairs that is sweeping professional sports."

"We have witnessed teams cavalierly abandoning, or threatening to abandon, their home town for other cities, often leaving in their wake a financially and otherwise distraught community," testified Sen. Thomas Eagleton (D-Mo.), cosponsor of one of the bills being considered.

Eagleton's bill, cosponsored by Sen. John Danforth (R-Mo.), would give football, basketball, hockey and soccer leagues the right to block the relocation of a team to a new city, pool network revenues to promote parity and select or terminate a team owner by the vote of a majority of owners. Major league baseball, which has an antitrust exemption as a result of a Supreme Court decision, would not be included in the Eagleton-Danforth bill.

All professional sports would be covered by a second, more controversial bill introduced by Sen. Slade Gorton (R-Wash.). That bill, establishing a federal arbitration board to rule on franchise disputes, would also mandate expansion by both the NFL and major league baseball.

"We want to pick our own cities when we expand. We want to pick our owners," said Rozelle, arguing against the Gorton bill. "I don't know of any business where the government can tell a company to expand, by how much, and in what years."

"It is the leagues themselves, and not the federal government or a regulatory board, that are best suited to weigh the variety of competing considerations and balance the numerous relevant factors involved in a proposed relocation," said the NBA's Stern.

Gene Upshaw, executive director of the National Football League Players Association, argued against giving team owners in the NFL any more power than they already have.

"Such decisions by sports owners should not be placed entirely beyond the law nor should they be permitted to be made by whim, caprice or personal prejudice . . .Past experience shows it is dangerous . . . There is no justification for further private special legislation for the sole benefit of the team owners," said Upshaw, who supported the provision in the Gorton bill that would establish a federal review board.

Members of the Senate committee, particularly Sen. Larry Pressler (R-S.D.), said the recent momentum of the committee had been toward deregulation of industries, and he feared the passage of either bill would "put us in the business of creating a federal sports bureaucracy."

Sen. Russell Long (D-La.) was less concerned with what the committee might be creating than with what his state might be losing if some type of bill is not passed. Recently, owners of the New Orleans Saints and the St. Louis Cardinals said they felt legally free to move to another city if they wished.

"We don't want to start all over again," Long said. "My thought is if somebody's got to start out with a new franchise and get stomped by all these big teams, it ought to be somebody else. If we want you to do the right thing, we've got to give you the power."

Perhaps the most titillating testimony for Washington fans was delivered by major league baseball's Hadden. When asked by committee members if the legislation under consideration might not "freeze the status quo," Hadden said baseball is "committed to expand . . . I would be surprised if we didn't add two additional teams before 1988."