Ask almost any serious young dancer, from Paris, France to Paris, Texas, where he or she would most like to work and the reply will shoot back in three syllables: NDT. Nederlands Dans Theater is the dream, a company that supremely combines the creative freedoms of modern-dance theatre with rigorous classical discipline. And it is lauded the world over.

Everywhere, that is, but Britain, a mere Channel hop from its base in The Hague. By some odd or devious mischance, it has set foot here only twice in the last 20 years, but last week the Edinburgh Festival had NDT's director Jiri Kylian belatedly sharing top choreographic billing with the Festival's darling Mark Morris. It may be invidious to compare the two: the American Mark Morris Dance Group is famous for its dancers that don't look like dancers; NDT's emphatically do. But as examples of what pure movement is capable of, to challenge as well as entertain, these two companies carry the flame.

Kylian's version of A Symphony of Psalms is a key work in NDT's repertoire, taking a typically bold sweep at a monolith of Western classical music. There are some stunning images: a line of figures swoops from stage left to stage right like a breaking wave that ends in a white spume of cart- wheeling skirts. The men leap with the zeal of young bucks, or surge forward like horned herds on the rampage.

Complex rhythmic footwork carves patterns in the great wall of Stravinsky's crunchy choral sound. Yet worryingly, Kylian has no answer to the Symphony's awesome, slow, breathed alleluja - a quiet chorus for peace. It might as well have been the rite of spring for all the sense of holiness it invoked on stage. So in the end Stravinsky's music is reduced, as if the process of visualising it has leeched away its terrible liturgical power.

The patchwork of Baroque (again, sadly not live but taped) that accompanies Kylian's newest work, Bella Figura, bode no better. But musical scruples are set aside in the face of potent physical theatre. Touching on Jungian theories of dreams and reality, adversities brand themselves onto the viewer's imagination. Topless dancers of both sexes - their lower halves clad in vibrant red crinolines - totter about like Japanese geishas; a naked girl emerges repeatedly from the curtains; couples dance sublime duets beset by an intangible angst. Even the frame of the stage (normally the audience's sure point of reference) erratically shrinks and expands like a zoom lens.

Kylian has the ability to stir dark and murky depths in a way that seems scarcely possible through dance alone. The piece by his protege Paul Lightfoot, though packed with coups de theatre and violent movement, looked callow by comparison. But NDT's extraordinary dancers - everyone a soloist - rivet the attention through thick and thin. NDT will return. I hear the Festival is already negotiating another visit with the stipulation that there will be more live music.

The delicious anticipation of an evening with Mark Morris Dance Group hangs as much on his choice of music as his choreography. This year's mixed bill imports a Javanese gamelan plus harp and trumpet into the pit for just one item - World Power, with score by the veteran West Coast hippy Lou Harrison.

Inspired by Mark Twain's denunciation of America's colonising of the Pacific, the work is unusually polemical for Morris - a man who once stated that politics don't make art. He should have stuck to his guns. Accompanied by the modal tinkling of bronze timpani, his dancers appear in an arch parody of temple dance, with stiff angled arms, fixed smiles and sweet little trotting runs. Ugliness intrudes with two warring males; native bodies thud to the floor and are dragged away as an imperial-sounding trumpet soars above the gamelan. If this sounds simplistic, it is. Though charming and clever in the way the dance matches the delicate monotony of the gamelan, and eminently watchable, the work does little to illuminate its source.

On his fifth consecutive visit, it was fitting that Morris should be the one chosen to mark the Festival's 50th birthday. Alongside two well- trodden works - a dazzling solo by MM himself in pink pyjamas and a piece danced in silence - he premiered I Don't Want To Love, a series of amorous vignettes danced to Monteverdi madrigals, sung and played by the Concerto Italiano. Dressed in flapping white bell-bottoms and babydoll dresses, dancers drift through romantic meetings and partings with the glowing purity of classical sculpture. Lavish but never flashy, expansive arms floating above smooth fiendishly fast feet, the work is a confection of light and delight. Morris has wowed Edinburgh yet again. How will they ever let him go?