Although Alonzo King LINES Ballet is a contemporary dance company based in San Francisco, its dancers’ classical training shows through in everything they do.

On its UW World Dance Series program at Meany Theater on Thursday, what also shone through their performance was King’s allegiance to the music he chose for his choreography. In each piece, King uses conventional ballet moves that morph into something unexpected and original.

The newest work on the program premiered last October. “Concerto for Two Violins” uses Bach’s Concerto in D Minor for those instruments and, watching the dancers, one could see the intricacies of Bach’s polyphony brought to life, each line of music or dance weaving through others in a never-ending flow of imaginative design. It was particularly noticeable in the slow second movement that used only four dancers: two men, two women.

All 11 company members are beautiful dancers, with strong feet that grip the floor or peel off it and a flexible fluidity of movement that mirrors the fluidity of King’s choreography.

An excerpt from his “Writing Ground,” to Sephardic music, is an odd piece for one woman and four men. It has a medical feel somehow. The woman, danced by Meredith Webster, begins floppy as a rag doll, supported by the men. As she gradually regains muscle tone in bursts, they support her moves, and when eventually she tries to escape they catch and bring her back. At the end, she sits on the floor laughing noiselessly. What it means I don’t know, but Webster’s moves are extraordinary, including one where she is raised horizontally by the men, then swoops down headfirst and backward into a swan dive.

“Rasa,” to live tabla and voice music of Zakir Hussain, goes on rather too long, the most compelling part being a duet between what appears to be two lovers enjoying a wrestling game. Oblique golden lighting by Alain Lortie effectively colors the work. At one point, the singer uses tonguing faster than a trill, and dancers achieve a torso shaking that matches, but none of it is obvious, it’s just part of the movement.

Costumes are simple, never obscuring the bodies. Men wear black or beige briefs, sometimes long pants, no tops. In “Concerto” the women wear backless black or pale beige swimsuits, and in the other works, brief gauzy tunics that hide nothing of a body’s workings. These and the sets, again simple but strong, are designed by company co-founder Robert Rosenwasser.