Even if you don’t like seeing a water bug scuttle across a counter, you may like Jerome Robbins’s “The Cage,” his 1951 ballet that was part of a new all-Robbins program that had its debut at New York City Ballet. “Generation Next” is made up of five ballets with pronounced novelty value.

In “The Cage,” we visit the hive of a colony of predatory female insects who perpetuate the sometime instinct of the entomological world in devouring their sex partners. The dancers are just as bug-like as can be, but they also seem like apes, sometimes. They also kick, thrash, pound, and assume the savagely large-scale displacements of Bacchantes in Balanchine’s “Orpheus.” Tanaquil Le Clercq, who inspired Robbins to make “The Cage,” had performed the Leader of the Bacchantes at the premiere of “Orpheus” in 1948. “The Cage” preserves the sapphic flavor of the mythical Bacchantes and Amazons, as the women partner each other more warmly than they do their unlucky male visitors. But “The Cage” is more than the sum of its source material; it’s an outlandish spectacle all its own. Robbins takes extreme liberties with the human figure: The rotations and inversions of the dancer’s four limbs in their sockets make the choreography seem proto-William Forsythe.

Teresa Reichlen was the Queen of these creatures, and Wendy Whelan was the Novice, and they were uncompromisingly worthy of fumigation. Adam Hendrickson and Sébastien Marcovici were their victims, and both men accepted their fate nobly.

What’s anomalous about Robbins’s “Moves” is that its 11 dancers perform to silence. Robbins made it for his own “Ballets: U.S.A.” in 1959, and it didn’t enter NYCB’s repertory until 1984. Silence becomes relative because, besides the incidental noises from audience and dancers, the dancers’ bodies make clapping and stomping sounds as their arms and legs perform the percussive actions he designed. The style of the ballet combines the Balanchine modernist manner with the Robbins school of alienated-adolescent jazz. But Robbins doesn’t seem to be making a ballet that investigates the possibilities of silence as much as he is making a ballet that has lost its soundtrack.

The novelty factor in “Four Bagatelles” is in its re-emergence onstage, after decades in dry dock. This duet was first performed in 1974 by Violette Verdy and Jean-Pierre Bonnefous, two great French dancers who eventually emigrated to NYCB. And there’s a lot of archetypal Frenchness in the choreography. Both dancers wear Baroque costumes designed by Florence Klotz. The man’s role seems to have been inspired by the reputed style of legendary late-18th-century French virtuoso Auguste Vestris, as well as by the ballets choreographed in Denmark in the following century by Vestris’s pupil August Bournonville. The man darts, bounds, alights while his ballerina puts a quick, finicky, coquettish finish on her phrases. Performed to a sheaf of lovely and slightly odd Beethoven piano pieces, “Four Bagatelles” on Tuesday proved itself well worth reviving. Neither Ashley Bouder nor Gonzalo Garcia seemed yet to have fully digested their roles.

The program opened with Robbins’s 1972 “Circus Polka,” performed by female students of different ages, before whom Robert La Fosse facetiously cracks a whip. It closed with “Fanfare,” which is customarily performed by professional dancers, but this season becomes a companion showcase to “Circus Polka” for the works-in-progress of NYCB’s affiliate School of American Ballet. “Fanfare,” is something of a lecture-demonstration performed to Benjamin Britten’s “The Young Person’s Guide to the Orchestra.” A majordomo talks us through the dancer’s kinetic illustrations of different instruments and schools of tonalities. The SAB students — intermediate and up — were diligent about keeping their bodies under proper discipline, and their excitement at being onstage created definite electricity.

Prior to “Circus Polka,” Robbins had choreographed “Dances at a Gathering,” which was performed last week as part of NYCB’s “Definitive Chopin” program. In “Dances at a Gathering,” his first work for the company since 1956’s “The Concert,” he again used Chopin music, as he had for “The Concert,” also included in “Definitive Chopin,” together with “Other Dances,” the duet he made in 1976 for Natalia Makarova and Mikhail Baryshnikov to dance as a gala.

In the program, the dancers are identified only by the color of their costume, and yet Robbins gives us readily apprehended character types, derived as much from musical comedy as from ballet. As he would again in “Other Dances,” he interjects choreographed stumbles that might derive from the way Fanny Brice and other headliners of Robbins’s youth would frequently perform ballet send-ups. Agnes de Mille had made hay with this device in Broadway’s vastly influential “Oklahoma!” on Broadway in 1943. In that musical, Joan McCracken was “The Girl Who Falls Down.” Halfway through “Dances,” Robbins introduces a new character, danced last week by Sara Mearns, who could well have been danced by McCracken. In her first solo, Ms. Mearns “in green” ignores musical notes, waywardly listening instead to herself. Later, she is pursued by three men in turn, each of whom finally finds her too flighty. Left alone, she takes it in stride, making a “Fiddle-dee-dee” flourish with her arms as she exits.

As much as he gives us identifiable character types and situations, Robbins takes pains to make things not fit together too neatly. One of the most potent devices in “Dances” is its carefully casual asymmetry. The ballet begins with Damian Woetzel alone, and closes with all dancers onstage — yet Mr. Woetzel is center stage.

Mr. Woetztel is retiring this season, and this was his last “Dances.” He made something distinct and memorable of each of his many different appearances, from his curtain-raising monologue, which projects something of the flavor of memento mori, to his more technical solo later in the ballet. Gesture came to the forefront in his duet with Yvonne Borree, where they made happy talk with their hands, and his mock competition with Mr. Angle, which he deflated with an “Oh, never mind” dismissal.

“Dances” lasts an hour, but Robbins’s invention doesn’t flag, nor does one’s attention. Yet when it’s over, one is ready for something smaller-scaled, and “Other Dances” arrives at just the right place in the program, following “Dances at a Gathering” and an intermission.

“Other Dances” was performed by Julie Kent, a guest artist from American Ballet Theatre, partnered by Mr. Garcia, who was making his debut in the ballet. It wasn’t the most comfortable performance, even allowing for the disparities that are written into the ballet. Mr. Garcia is of medium height, and Ms. Kent is tall. When he lifted her on Friday, you frequently couldn’t see him at all, and their final lift was precarious. Considered as a debut performance and special occasion pairing, their work was fine. Nevertheless, their performance lacked the ultimate in impulsiveness and, musically, they were too square: They couldn’t dance through the music in the way that Robbins intended.

In the closing “The Concert,” jokes and charades and fantasies were all as funny as ever, yet much of the cast was new to the ballet, and it showed. If this had been one of the many musicals that Robbins choreographed and directed, this “Concert” could have been an encouraging tryout performance.