Tape recordings of private conversations between President Nixon and associates during the Watergate crisis will be made available for public listening at the National Archives here starting Wednesday.

On a first-come, first-served basis, the public will be permitted to hear 31 tapes, including 30 that were played in open court during the 1974-1975 Watergate cover-up trial.

The archives, which has custody of Nixon's presidential materials, said 24 listening posts will be set up where the tapes may be heard in its building at Eighth Street and Pennsylvania Avenue NW.

The tapes, which total 12 1/2 hours, have been grouped into 15 segments, which will be played in sequence over a four day period, then repeated.

Based on the length and groupings of conversations within the overall sequence, the number of listening sessions each day will vary from two to five.

Beginning Wednesday, free tickets for use of the 24 individuals listening posts will be made available, each day, Monday through Friday, in the Archives lobby.

Thirty of the tapes, recorded in the White House and Executive Office Building, were made over a period beginning June 23, 1972 -- six days after the break-in at the Democratic headquarters -- and ending April 19, 1973.

These recordings were played in the U.S. District Court here during the trial of five high-ranking officials of the Nixon administration for their alleged roles in a conspiracy to obstruct the investigation of the break-in.

The tapes, regarded as significant prosecution evidence in the trial, which ended with four convictions, were themselves a matter of considerable legal controversy. They were surrendered only after a long effort to withhold them.

Copies were turned over to the Archives by the District Court in 1978. They are now being made available "for research," the Archives said, after congressional approval of access regulations drawn up by the Archives.