A telephone sweepstakes offering one lucky American a chance to ride on the Soviet space station hit a snag when a flood of calls from aspiring cosmonauts overloaded the circuits.

Each $2.99 call to the 900-number gives the caller a chance to win six months' training, a trip aboard a Soviet rocket and a week on the space station Mir in 1992 or 1993, said Space Travel Services, the company promoting the offer.Thousands of calls Monday, the first day the line was open, overloaded the circuits. The line was expected to be working again early Tuesday.

The winner, to be selected in a drawing in December 1991, gets the trip plus $500,000 in cash or can forgo the trip and take $1.5 million.

"Our long-term business strategy is to arrange for space travel opportunities for anyone who wishes to go into space," said James Davidson, senior vice president of Space Travel Services.