Zubin Mehta, music director of the New York Philharmonic since 1978, will step down at the end of his current contract, which extends through the 1990-91 season. At that time he will have held the post longer than any other conductor in the orchestra's modern history.

The search for a successor is on, and among the names being mentioned is Charles Dutoit of the Montreal Symphony; also Leonard Slatkin of the St. Louis Symphony and Giuseppe Sinopoli, frequent guest conductors. Mehta has declined several music director offers, saying he wishes to pursue a less administrative career, and he has signed for several opera projects in Europe beginning in 1991.Mehta has not been a favorite of critics in New York, being considered on the prefunctory side, and has seldom led major recordings of the Philharmonic. Those assignments have gone recently to Leonard Bernstein, the Philharmonic's laureate conductor, or Sinopoli. However, Mehta has maintained the support of Management, board and public, for about 90 percent capacity at Avery Fisher Hall. And he has overseen a major transition of orchestral personnel. Because of an unusually large number of retirements, 36 new members have joined during his tenure, including concertmaster Glenn Dicterow and 10 other first desk players.

-FIVE INDIVIDUALS have been selected to receive the Kennedy Center Honors for 1988 in Washington, D.C., on Dec. 4. They are choreographer Alvin Ailey, actor George Burns, actress Myrna Loy, violinist Alexander Schneider and Roger L. Stevens, founder of the National Endowment for the Arts and the Kennedy Center.

-DAVID DEL TREDICI, composer of "Final Alice" and winner of the 1980 Pulitzer Prize for his "In Memory of a Summer Day," has been named composer in residence of the New York Philharmonic. His two-year assignment will include writing a work for the 150th birthday of the orchestra in 1992.

The appointment is part of the Meet the Composer Orchestra Residencies Program. Other composers so honored this year are Robert Beaser, American Composers Orchestra; Donald Erb, St. Louis Symphony; Stephen Paulus, Atlanta Symphony, and Steven Stucky, Los Angeles Philharmonic.

And Andre Watts, American pianist, has received the Avery Fisher Prize, in recognition of outstanding achievement and excellence in music. He received $25,000 cash, and his name will be inscribed on a marble plaque in Lincoln Center's Avery Fisher Hall. Watts recently celebrated his 25th anniversary as a concert artist.

-CONNECTICUT ORCHESTRAS are deadlocked in long-lasting strikes. The New Haven Symphony, a part-time orchestra, rejected management's proposal and walked out in mid-October. And members of the Hartford Symphony Orchestra are on strike for higher wages.

-THANKS TO JAPAN, Egypt has replaced its destroyed opera house with a $50 million complex that recently premiered with the first performance of Kabuki theater on the Nile.

-THE MARTHA GRAHAM DANCE COMPANY, which recently concluded its fall season at New York's City Center, featured some interesting guest artists for its opening performance. These included actress Kathleen Turner as One Who Speaks in a Graham masterpiece, "Letter to the World." Reportedly, Turner gave a surprisingly good account of herself dancing. Also onstage were Mikhail Baryshnikov as the Christ figure in "El Penitente," and Russian ballerina Maya Plisetskaya, dancing her famous "Dying Swan."