Five years after winning a much-publicized lawsuit over the rights to Martha Graham’s works, the dance company Graham founded struggles on. Still fighting its way out of a massive debt, the beleaguered troupe will spend much of this year touring to pay the bills. Sadly, there will be no true New York season in this, the company’s 80th anniversary year — just a series of one-off performances like Wednesday night’s free concert, part of Lincoln Center Out of Doors.

Wednesday night’s performance of four Graham works testified both to the company’s glimmering potential and to its very real problems. The capacity crowd of 6,000 eager spectators was proof of the enduring appeal of Graham’s work, and the committed dancers (who have stuck by the financially strapped troupe) made sections of each dance crackle with life. Unfortunately, stretches in each piece displayed dancing that was either rough or dated, and these brought down the overall level of performance. It didn’t help that the company’s most effective interpreter of Graham, the marvelous Fang-Yi Sheu, was on temporary leave, performing abroad. Katherine Crockett, another principal, was absent due to injury.

The question now facing artistic director Janet Eilber (who was appointed a year ago, in yet another controversial development) is how to draw contemporary audiences into dances whose dramatic, expressionist effects may not work as well as they did in Graham’s day — or may not work as well without Graham herself in the lead role. Ms. Eilber has stated that she intends to reach out to contemporary audiences, and Wednesday night, both she and dancer David Zurak took turns introducing Graham’s works to the massive, heterogeneous crowd.

Mr. Zurak described the 1936 sketches from “Chronicle” as a “timeless anti-war message,” while Ms. Eilber said that “Diversion of Angels” (1948) was “all about love” and featured “either three different women, or one woman at different times in her life.” These introductions had an easygoing, friendly quality, reminiscent of a high school English teacher who encourages you to discover poetry.

Of course, interacting with audiences is only a small part of Ms. Eilber’s strategy; her main task is to create fresh (or at least, not fusty) interpretations of classic Graham repertoire. First up were the sketches from “Chronicle,” made for Graham’s early, all-female company. In the opening solo,”Spectre: 1914,” Elizabeth Auclair swung her long dark hair, cupped her fists, extended her leg high beneath her billowing skirt, then engulfed her head and body with the skirt’s blood-red lining. It was a quintessentially Graham stage picture, but while the technique was there, the performance lacked puissance.

The second section, “Steps in the Street,” began with a group of defiant black-clad women backpedaling slowly across the stage. Here the balled fists and proud necks communicated a palpable ferocity. In the finale, “Prelude to Action,” Ms. Auclair looked wiry and purposeful as she stood atop the podium in a classic Graham dress with a black-and-white graphic pattern. The female ensemble’s hard-edged motions and quick, hurdling leaps gained speed and built to a striking conclusion, with Ms. Auclair’s arms rising as the others’ arms fell.

Though “Sketches from ‘Chronicle'” felt far from contemporary, the piece had a convincing immediacy. This was confirmation for those who argue that Graham’s sharp movements and strong stage pictures need only to be performed with uncommon conviction, rather than updated.

“Diversion of Angels,” one of Graham’s most durable pieces, held the same promise, but its lyrical, light quality was marred by the dancers’ unsteadiness in what should have been stunning balances. There is still much to feed the eye in “Diversion” — the girl in red (Alessandra Prosperi) dashing across the diagonal, ducking, then tossing her head back; the shock of an unexpected lift; the curious shape of the men’s legs as they hop around the stage. But the performance failed to capture the all-out joy of the piece.

Likewise, in Virginie Mecene’s performance of “Deep Song,” a solo from 1937, the flesh was willing, but the spirit was weak. And the first section of “Acts of Light” (1981), with its nearly nude dancers gamely getting through a dated duet, felt inevitably stale.

How gratifying, then, to see the company’s evocative dancing in the final two sections of “Acts of Light” (1981). Miki Orihara showed an intense, believable concentration in “Lament,” turning supple back-bending falls and arresting stillness into voluble expressions of grief. In “Ritual to the Sun,” the assembled company of dancers seemed to be taking a class, moving steadily in unison through a series of calisthenics, the skin-tight gold Lycra showing their every muscle. Yet somehow these familiar Graham movements, paired with Carl Nielsen’s stirring score, had an inexplicably poignant charm. As the dancers surged from one motion to the next, the pleasure of pure movement reflected slightly differently on each alert face. There was something very un-Graham in this sequence: a hushed humility.

In the troupe’s finest moments Wednesday night, one glimpsed a future for the Martha Graham Dance Company: that of a living archive that preserves classics not merely for the sake of tradition or history, but because they continue to move and provoke audiences. However, the uneven performances showed that when dancers lack that crucial vitality, Graham’s choreography can quickly feel dated and remote.