Dancers from Alvin Ailey American Dance Theater perform "Revelations." (PAUL KOLNIK/PAUL KOLNIK)

New beginnings often contain built-in excitement, but there was an extra note of promise in the Alvin Ailey American Dance Theater’s program Tuesday night at the Kennedy Center Opera House. This was Washington’s first look at the effects of a change in leadership at the company, and going by the pleasant surprises in the repertoire, as well as the healthy appearance and vivid energy of the dancers, Artistic Director Robert Battle has the troupe’s forward momentum well in hand.

We’ll have to wait for future seasons to see if Battle, who officially took over from longtime director Judith Jamison in July, has any major alterations in store for the 53-year-old modern-dance company. It’s unlikely that he will deviate much from Ailey’s consistently winning formula of a lean touring operation — unencumbered by elaborate sets or costumes — and accessible works capped by “Revelations,” a gospel-driven distillation of human vitality created by founder Alvin Ailey. As expected, that piece will close each of the troupe’s performances during its stay here, which will end Sunday.

Although Tuesday’s program showed no radical inclination toward a break with the company’s past, there was one important, and perhaps momentous, development. For the first time in its history, the troupe performed a work by the venerable Paul Taylor. And even though that piece, “Arden Court,” was not perfectly rendered — the men need to soften their landings, and a few cut short the full expression of grandeur in the arms — it was certainly given respectable treatment.

Performing Taylor signaled that Ailey could transition into what the modern-dance world urgently needs: a repertory company to safeguard great but imperiled choreography.

Greatness doesn’t last long in dance, tied as it is to human mortality. We’ve lost Martha Graham (she died in 1991), and although her company continues on, it does not have nearly the reach of the widely touring Ailey operation. We’ve lost ­Merce Cunningham (he died in 2009) and his company (it disbanded in December). The influential German choreographer Pina Bausch also died in 2009, and her company’s future is uncertain. Not even the triumphant new Wim Wenders documentary about it is a substitute for live performance of Bausch’s work. We needn’t mourn Taylor yet — he is still creating. But he’s 81. And the reality is that any single-choreographer dance company is a fragile thing once its founder has died and there are no more premieres to attract funders and ticket sales.

Ailey’s great strength is that it takes on the works of so many choreographers. As a repertory company not wed to any one style or aesthetic, always seeking new blood, it was able to survive its own founder’s death in 1989. Yet the quality of offerings has not been stellar in the past several years — too much fishing in the familiar waters of company members trying their hands at dancemaking, or works that exploited physical feats over interpretive revelations. For this reason, Battle’s acquisition of Taylor’s “Arden Court” is a boon.

But “Arden Court” raises tantalizing what-ifs: What if Ailey acquires more great works by Taylor, Graham, Cunningham and others it has never essayed? What if it builds on “Arden Court,” to become a home for orphaned masterworks by the field’s eminences?

The idea of a national modern-dance repertory company has come and gone over the years — raised most recently by Peter Martins, the New York City Ballet’s ballet master in chief, who tried to get one started in 2004 — but has never caught on. Yet here is Ailey, well-funded, with its major audience appeal and its stable of multitalented dancers. Bravo to Battle for extending their reach. The more they dance Taylor the better, I say.

The light romanticism of “Arden Court,” danced to a baroque score by William Boyce, will surely improve with time, as the dancers take on its noble shapes with less effort and more fullness. But the Ailey dancers absolutely possess the fine-tuned, grounded athleticism to do well in Taylor’s works — more so, in fact, than the classical ballet dancers who tend to undercut the fine balance between weight and buoyancy that Taylor demands. Outside of the Paul Taylor Dance Company, ballet companies are the primary repository for Taylor works. The Ailey dancers’ understanding of weight and gravity is another reason to hope that more Taylor comes their way.

Another bonus Tuesday was the return of dancer Alicia Graf Mack, a tall, leggy native of Columbia, whose musical fluidity was one of the company’s chief assets a few years ago. Injury and university studies kept her off the stage, but Battle has brought her back. Her elegant line added distinction to “Arden Court” and Rennie Harris’s “Home,” a good-humored, friendly work that was so nice and warm — with dancers forming groups, trios, duets, passing around steps as though they were exchanging gifts — it didn’t have much of a focus. Battle’s bonbon of a solo, “Takademe,” sent Kanji Segawa shivering and bucking into the air as if a bee had gotten into his red Missoni-designed pants. It was great fun, a frisky palate cleanser. Primed one to see something other than the faithful warhorse “Revelations,” which followed. Perhaps that will be a future Battle reform: another ending. Even just once in a while.