Gustav Holst's "The Planets" will be a highlight of the National Symphony's program this week, with Andrew Litton conducting. Shura Cherkassky will be the soloist in Tchaikovsky's Piano Concerto No. 1, and the program will include Gershwin's Cuban Overture.

Pianists of the week:

Leon Fleisher, who will conduct and solo (in music for the left hand) with the Theater Chamber Players, Saturday and next Sunday in the Terrace Theater.

Earl Wild in an all-Liszt program this afternoon at the Kennedy Center. Theodore Lettvin at the Phillips Collection, which celebrates the 30th anniversary of its concert series today.

Steve and Nadya Gordon in a two-piano program of Mozart, Ravel, Gershwin, Stravinsky and Rachmaninoff, Wednesday night at George Mason University.

Jose Luis Caceres, performing Godowsky, Soler, Schubert and Liszt, Tuesday night in the Terrace Theater.

Ann-Marie McDermott, guest soloist with Alexander Schneider and the Brandenburg Ensemble, Wednesday night in the Terrace Theater.

Free concerts today include members of the Marine Band in their annual chamber music series, this afternoon at the Library of Congress, and the American Camerata for New Music, playing works of Jerzy Sapieyevski, Darius Milhaud and Kurt Weill, this afternoon at the Van Ness campus of UDC.

Other concerts today:

The Alexandria Symphony at T.C. Williams High School; the Arlington Symphony at Kenmore Auditorium; the Chamber Soloists of Washington at National Presbyterian Church; and the Manchester String Quartet with clarinetist Loren Kitt at the Holton-Arms School.

The Smithsonian Chamber Players will perform piano trios of Dvora'k, Tuesday and Wednesday evenings in the Hall of Musical Instruments. Dvora'k will also be on the Beaux Arts Trio's program (with Haydn and Faure'), Thursday night at the Library of Congress.

Other noteworthy concerts of the week include the Empire Brass, Friday night in the Terrace Theater; violinist Joshua Bell with pianist Angela Cheng, Saturday afternoon at the Library of Congress; and the Fairfax Symphony, with soprano Irene Gubrud, Saturday night at Fairfax High School. DANCE

The Dance Theatre of Harlem continues its run at the Kennedy Center Opera House, introducing two more programs this week and repeating all four before the visit ends next Sunday.

American Ballroom Theater offers its final two performances this afternoon and evening in the Kennedy Center Terrace Theater. The Dance Place series continues, now that the organization has lost its Adams-Morgan residence and is moving to the Brookland neighborhood, with a performance Friday night at Mount Vernon College's Hand Chapel, by the New York-based dancer-choreographer duo, Art Bridgman and Myrna Packer.

The Third Annual Choreographer's Showcase, cosponsored by the Jewish Community Center and the Maryland-National Capital Park and Planning Commission, Prince George's County, Arts Division, will offer three awards totaling $1,200 to winners among the seven works by area choreographers in the event. The showcase takes place Saturday evening at the Prince George's Publick Playhouse. FILM

Tuesday at 7:30 at the Library of Congress' Mary Pickford Theater, a rare kinescope of Peter Brook's legendary production of "King Lear," starring Orson Welles. A must-see.

"Shoah," Claude Lanzmann's epic documentary on the Holocaust, will be showing at the Jewish Community Center of Washington from tomorrow through the 23rd. Call 881-0100 for details.

The "Insult/Integrity: Historical Analysis of Blacks in American Cinema" series continues Thursday at 6 at the Martin Luther King Library. Free. Call 727-1271 for details.

The French Film Festival continues at the K-B Janus with "Tout Feu Tout Flamme," starring Isabelle Adjani, today and tomorrow. Consult your local listings.

Among current releases, Woody Allen's masterpiece, "Hannah and Her Sisters"; at the Key, "Huey Long," Ken Burns' documentary about the quondam Louisiana politico. POP MUSIC

One of the premiere post-punk bands in America, Hu sker Du , is the latest discovery from Minneapolis (after seven consistantly challenging records on small independent labels, the group has been signed by Warner Bros.). The band'll bring its sound of surprise to the 9:30 club tonight.

Phantom, Rocker and Slick sounds like a great band name but it happens to be the surnames of Jim Phantom and Lee Rocker (formerly of the Stray Cats) and guitarist Earl Slick (ex-Bowie), who have teamed for some raucous rock 'n' roll. At the Bayou on Thursday.

Lawrence (Buckwheat) Dural is the reigning champion of Louisiana's zydeco sound, which blends black R&B with traditional French music styles into an infectious, foot-stomping stew. He'll bring his Il Sont Partis band to the Roxy on Thursday.

Jazz clarinetist Benny Goodman is alive and well and, best of all, playing again. On Saturday, he'll be working in a context that's been rare in the past decade -- with a big band -- at the Kennedy Center Concert Hall.