The National Symphony Orchestra will go on a whirlwind tour of Europe next month, giving concerts in nine cities of Belgium, France, Switzerland and Germany between Oct. 11 and 21, orchestra President Albert J. Beveridge announced yesterday.

The tour, costing an estimated $900,000, will be a deficit operation, as such tours always are. The balance of the costs -- after the orchestra's income from the tour is subtracted from its expenses -- will be paid by Northern Telecom, an international telecommunications equipment manufacturer. Northern Telecom, which maintains corporate headquarters in Toronto, is setting up an American base in Vienna, Va., and says it plans to make extensive financial contributions in the Washington community.

This will be the orchestra's second overseas tour within eight months and its 10th (not counting six North American tours and four to the Casals Festival in Puerto Rico) during the 14-year tenure of music director Mstislav Rostropovich. In February the orchestra toured Japan and the Soviet Union -- in Rostropovich's first visit to his native land since he was exiled in 1974.

Northern Telecom's CEO, Paul G. Stern, said the sponsorship "is part of our 60th-birthday present to the National Symphony." Under Rostropovich's leadership, he said, it has become "one of the world's most acclaimed orchestras and one of the most admired in America." A year ago, Northern Telecom donated a business communications system valued at $1 million to the Kennedy Center, and Stern said the corporation is also interested in "supporting civic organizations and public service programs: hospitals, schools, environmental groups, cultural groups and a wide variety of nonprofit agencies."

The tour will include concerts in Brussels and Leuven in Belgium; Paris and Strasbourg in France; Zurich, Switzerland; and Bonn, Duesseldorf, Cologne and Hanover in Germany. The repertoire for the tour will be mostly music of Tchaikovsky (Symphony No. 4, the Serenade for Strings and "Romeo and Juliet"), but the orchestra also will play Mozart's Symphony No. 39, the Mussorgsky-Ravel "Pictures at an Exhibition," Shostakovich's 10th Symphony and Barber's Adagio for Strings in some programs. The orchestra will fly to Brussels on Oct. 8 and return from Hanover on Oct. 22.

Beveridge gave credit to Kennedy Center Chairman James D. Wolfensohn for securing the sponsorship. "His work on behalf of the orchestra has been vital to our success," he said in a press release. "He really hustled this one," he said at the press conference. Overseas tours and recordings, he added, "are very important for the orchestra's image."

Rostropovich, who will conduct all the concerts on the tour, also praised Wolfensohn ("we have financial sickness, but here is a very good doctor") and smiled politely when Stern described him as "also a cellist of some note."