THE NATIONAL tour of the Broadway hit "Other People's Money" is closing in Detroit, so the June stop at the National Theatre won't happen. Producers say the show is being "redesigned to facilitate travel," and that the tour will resume in the fall; there's no replacement for the National slot yet.

GREETING SEASONS: Following its most successful season ever, with all four productions -- including the current "The Merry Wives of Windsor" -- playing to over 100-percent capacity houses, the Shakespeare Theatre at the Folger has announced a star-heavy 21st season for 1990-91. Stacy Keach will open the season as "Richard III," directed by artistic director Michael Kahn. Avery Brooks, most recently seen in Washington as the lead in "Paul Robeson" at the Kennedy Center, will star in "Othello" in November, directed by Harold Scott, who plans to cast actors of color in the roles of Iago and Emilia. Rene Buch, artistic director of New York's acclaimed Repertorio Espanol, will direct Lope de Vega's "Fuente Ovejuna," in a new translation by Adrian Mitchell. Philip Bosco will close the season majestically as "King Lear" in April. Call 546-4000.

THE STUDIO Theatre's lineup will start off with Eric Overmyer's "In Perpetuity Throughout the Universe," followed by Giles Segal's "The Puppetmaster of Lodz," and Romulus Linney's "Unchanging Love," an adaptation of a Chekhov story. Studio's season also includes Charles Dickens's "A Tale of Two Cities"; the Shakespeare Theatre's marvelous Floyd King, so funny in the quick-change "Mystery of Irma Vep" at Studio, will perform the one-man adaptation by Everett Quinton of the Ridiculous Theatre Company. The title of Ntozake Shange's play is sure to be a favorite with copy editors everywhere: "spell //7: geechee jibara quick magic trance manual for technologically stressed third world people." The Studio will also bring in the puppet master/performance artist Paul Zaloom and his "The House of Horror."

The theater has also announced its upstairs, alternative Secondstage season, which includes Jim Cartwright's "Road," an environmental theater piece that takes the audience on a walk down a road in northern England; "Oil City Symphony," a musical along the lines of "Pump Boys and Dinettes"; "From the Mississippi Delta" by Endesha Ida Mae Holland; "Three Guys Naked From the Waist Down," a musical about three stand-up comics; and "Revolutionary Witness: Faces From the Fire," recollections of four French Revolution figures. Call 332-3300.