The dancers of the Royal Danish Ballet are must-sees on their too–rare visits to New York environs, the most recent being a week’s stay at Jacob’s Pillow. (By now it has been decades since the full company has visited New York City.) The core of the RDB repertory is the 19th-century ballets of August Bournonville, in which the same classical steps visible in Russian classics are swathed through space at different angles, in different sculptural configurations, and with perpetually mobile feet and a unique rocking horse back-and-forth momentum. At Jacob’s Pillow there were some noticeably long and lithe dancers, but the concentration on line that has been pursued obsessively in ballet cultures to the west and east of Denmark is not de rigueur at the RDB, and for good reason: the Bournonville aesthetic, which leans more to the village square than the royal salon.

The 12-member RDB delegation that came to the Pillow was organized by Ulrik Birkkjaer and Sebastian Kloborg, two company members barely out of their teens. Mr. Kloborg is the son of current RDB director Frank Andersen, who is soon to be succeeded by current New York City Ballet principal dancer and RDB alumni Nikolaj Hübbe. At Jacob’s Pillow, both Messrs. Birkkjaer and Kloborg cast themselves liberally but not undeservedly in the mixed bill they presented. Indeed, Mr. Kloborg’s and Mads Eriksen’s anything-you-can-do-I-can-do-better Jockey Dance from Bournonville’s “From Siberia to Moscow” was a high point of the program.

One doesn’t have to be a RDB product to master Bournonville. Indeed some of the best Bournonville performances I’ve ever seen have been danced by non-Danes. But there is special pleasure in seeing the Danes dance their time-honored repertory, and not just because they are products of an heirloom tradition. In watching virtuoso excerpts from the Bournonville repertory, it is evident that the characteristic high spirits and bonhomie of the Bournonville aesthetic have become a ritualized state of theatrical existence, different from but comparable to the formalized elegance and authority of the Russian classical style.

The RDB dancers have so much spirit, individuality, and belief in what they are doing that it didn’t matter that few of the dancers seemed to be performing at his or her full capacity on Friday night. Pirouettes came undone all over the place, though this may have been due to the disorientation produced by dancing on Jacob’s Pillow’s flat stage rather than the company’s raked stage at its old theater in Copenhagen. The Pillow stage is also much smaller than the company’s stage at home and the dancers seemed hamstrung by the stage dimensions. In addition, the incarnation of the company here included many very young dancers, two or three years away from their graduation from the RDB school; some were given opportunities to dance roles above their current company repertory and thus beyond their current security level. But that’s part of the charm and part of the rationale for a summer tour such as this.

A troupe that is as much defined by its heritage and tradition as the RDB places great and perhaps excessive stock in the opportunity to dance anything less than 100 years old, and so we also saw several less distinguished but more recent works than those in the Bournonville canon.

The choreography of former company director Harold Lander was represented by his “Festival Polonaise” pas de deux, which dates to 1942. His strange combinations — crowning bravura end stops are placed in the middle of phrases — are perhaps meant as parody. Coping with the ungratefully-composed phrases were Gudrun Bojesen and Mr. Birkkjaer.

Two more recent works continued in the ebullient mode of adolescent discovery that characterizes so much Bournonville, but here the choreographic antics seemed archly puerile. “My Knees Are Cold,” a world premiere by young company member Louise Midjord, was titled appropriately, as the four-person cast wore shorts. To a sampling of contemporary beats the dancers comported themselves Raggedy-Ann style. In Tim Rushton’s “Triplex,” which the company had shown during its 2004 American tour, three dancers did a lot of fanny-wagging and posturing set to Bach.

Everyone in this splinter troupe came out for the finale, which contained excerpts from Bounonville’s “Napoli,” that are a traditional end to these type of RDB highlights tours. “Napoli” presents a kinetic manifestation of the Northern Europeans’ fascination with the sunny South. The festive Pas de Six and the hybrid Italo-Dane Tarantella that followed functioned beautifully as a summing up of the world of Bournonville.