The plot twists and historical events surrounding the collaboration between Balanchine and Stravinsky have all the trappings of a great romance, or at least a friendly rivalry.

The two men grew up in St. Petersburg. Each showed a predilection for the other’s art form: Stravinsky savored ballet more than music, while Balanchine trained in earnest as a future concert pianist. When they eventually succumbed to their natural gifts, they brought to their art not the didacticism of a born believer but the enthusiasm of a convert. As a result, both men displayed a cross-disciplinary creative fancy; their range spanned three continents and encompassed several artistic orthodoxies.

Nowhere is this more apparent than “Agon,” which concluded the New York City Ballet’s All-Stravinsky program on Wednesday. The Greek word for “contest,” “Agon” here does not suggest any action onstage as much as between the two collaborators. Set to a score specially commissioned by Balanchine, the work pitted choreographer and composer against one another, as they tested each other’s ingenuity.

Both ventured into the other’s territory. Stravinsky took as the model for his music an obscure dance manual from the mid-17th century; likewise, Balanchine adopted musical structures such as the canon pattern and fugue-like variations. The score, performed this week under the baton of guest conductor Clotilde Otranto, is Stravinsky at his most rhythmically complex. It is filled with historical references to other composers, unlikely sonorities, and tonal quirks. Balanchine strived to match the difficult score with punning and often strangely enchanting movements of his own.

In the opening measures four men in stark black and white leotards breezily march, indicating quick transitions with a swivel of their hips. The dancers are nearly reduced to mathematical integers, tapping their feet around feelingly. Balanchine used to beat time on a rehearsal chair, alternating between four counts of three, or three counts of four. Fittingly, then, Part I features a single, double, and triple pas de quatre.

Amar Ramasar and Andrew Veyette are both new to the work. With the imminent departures of Peter Boal and Jock Soto at the end of this season, Mr. Ramasar and Mr. Veyette represent the next generation of dancers to inherit the piece. They both held a strong presence, darting into challenging maneuvers with poise and balance. On one foot, they rotated like figures on a carousel in a display case during the second pas de trois.

The steps became increasingly elaborate, leading up to the memorable duet. The combinations put Mr. Soto on his back, scuttling his feet. Eventually he spread completely out on the floor, supporting Wendy Whelan in a deep arabesque. To the sound of a harp, he folds up his body like an origami doll, all the while maintaining a convincing poker face.

Mr. Soto’s partnering skills were also vigorously on display in Jerome Robbins’s “The Cage.” Stravinsky’s darkly insinuating Concert Grosso in D for Strings accompanies this re-enactment of the predatory habits of insect life. Mr. Soto played the unlucky second Intruder, entering beneath Jean Rosenthal’s giant, hanging web. He confronts the Novice, performed by Ms. Whelan in a black short-cropped wig. Ms. Whelan follows a glamorous line of ballerinas, including Allegra Kent, Melissa Hayden, and Tanaquil LeClercq, in this role. She curls up spinelessly in her opening solo and heaves wildly for air.

In the image of the immature pupa, Robbins found a perfect candidate for grotesque contortions. He faithfully reproduced insect behavior with scampering walks and fang-like arms. The Novice hunts the first male she sees, stabbing him with her pointe shoe, and strangling him between her knees. But once Mr. Soto enters, dark and handsome, her movements become recognizably human. As he approaches she is absorbed. He holds her tightly, and she floats swimmingly downward. In a moving reversal, he holds her between his legs, and they each spread their arms out in parallel horizontal lines.

“Concertino,” another Robbins work, set to selected chamber music by Stravinsky, was originally commissioned for the Stravinsky Festival in 1982. Here Robbins explored the possibilities of movement between three dancers; on Wednesday these were Sofiane Sylve, Ask la Cour, and Stephen Hanna – all new to their roles. Although each gave a committed performance, this remains one of Robbins’s lesser works, looking somewhat like a chore. They gesticulate with their limbs in close proximity, hooking arms, and stepping over one another. They divide quick, felicitous phrases with slower, almost surgical poses.

The evening began with Stravinsky’s homage to Tchaikovsky in “Divertimento,” a musical suite from the ballet d’action “Le Baiser de la Fee,” first staged by Balanchine in 1937 for the American Ballet. Based on Hans Christian Andersen’s fairy tale, “The Ice Maiden,” the ballet originally consisted of a single act of four scenes. In Stravinsky’s mind, there was a parallel between the Ice Maiden’s kiss and the Muse’s blessing of Tchaikovsky – a musical inspiration that eventually proved fatal.

Stravinsky ultimately restructured the work as merely a “Divertimento.” The final form as it appears in the NYCB repertory departs from the story almost entirely, only hinting at the scenario and doing away with any set design. Wearing peasant skirts, a corps of village girls entered into a round dance upon the arrival of Megan Fairchild, whose faultless phrasing as the bride-to-be was breezy and pert opposite her beau (Joaquin De Luz).

In her solo Ms. Fairchild lazily follows through the closing of a turn, her arms perfectly lackadaisical above her. Captured in a daydream, she forgets herself in the midst of multiple pirouettes. For his part Mr. De Luz improvises joyous leaps in his solo, rising in the air for a turn with his heels touching. He closes with darting phrases to the four corners of the stage, overcome by a vision.

The brisk corps work occasionally faltered in the uneven rowing gestures of the arms. But “Divertimento” had a heart at the center, owing to the moving final duet. Approaching each other from across the stage to the boding warning of a cello, Ms. Fairchild and Mr. De Luz cautiously promenade. As their movements become more urgent, they bend backward, but fail to reach. The closing apotheosis, which once contained elaborate stage magic, is achieved without the Ice Maiden’s magic at all. In a compelling image, both dancers quietly exit in different directions, their palms upturned, holding a beam of light.

“The Cage” and “Concertino” will be performed again June 4 & 7; “Agon” will be performed again June 5 (Lincoln Center, 212-870-5570).