MOSCOW, SEPT. 28 -- Washington and Moscow are working on improving their relations, and they are going to start with a little song and dance.

The thaw under discussion is not between the two superpower countries, but between their two capitals, which are looking ahead to a full program of cultural exchanges to begin in January.

The original idea, broached by the Washington, D.C.-Moscow Capital Citizens Exchange, a private group working with the support of Mayor Marion Barry and the D.C. Council, was to explore the establishment of a sister-city relationship.

But halfway through its visit here last week, the Washington group learned that Moscow does not have sister cities, just bilateral relationships. "Peculiarities exist everywhere," explained Georgi Dyakov, external relations officer for the Moscow City Council, or Mossoviet.

Undeterred by technicalities, the Washingtonians lobbied their cause and left town with tentative commitments for a full range of cultural events that could start as soon as next year's Martin Luther King Jr. holiday.

"We were told they hold King in great reverence here, too," said Theodis R. (Ted) Gay, cochairman of the District's Commission on the Arts and Humanities.

Fritzi Cohen, president of the citizens exchange and partner in the Tabard Inn, established the group in 1985 as an offshoot of the peace movement.

It now has 300 members and is operating with funds raised last summer at a party held in honor of the visiting Bolshoi Ballet.

"In looking for a way out of the nuclear dilemma, sister cities seemed like a natural," said Cohen, who is also chairman of the mayor's Nuclear Freeze Advisory Board.

The Washington delegation, hosted here by the Mossoviet, also included Clifton B. Smith, the District's ombudsman, and Jan Rothschild, a special events organizer for the exchange.

Typically, establishment of a sister-cities project starts with an exchange of visits by the mayors. In this case, the two sides are contemplating a satellite hookup between the two capitals in which Barry and Moscow Mayor Valery Saikin would participate.

Washington already has sister-city relationships with Beijing; Dakar, Senegal; and Bangkok, and less formal ties with Brussels. Moscow, which is not a member of the International Federation of Twin Cities, has relationships with 70 cities around the world.

So far in the negotiations, Washington has been the one to come forward with concrete proposals -- which range from visits to Moscow next year by the vocal group Betty, poet Reuben Jackson, filmmaker Michelle Parkerson and the Ajax Moving Company, a dance group.

Other ideas included a dialogue on environmental issues, exchanges of photo exhibits, jazz and theater groups and visiting artists.

To maintain symmetry, Moscow will appoint an equivalent citizens group to select Soviet groups and shows that will pay the return visit to Washington.