Polyrhythm (/ˈpɒlirɪðəm/) is the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. The rhythmic layers may be the basis of an entire piece of music (cross-rhythm), or a momentary section. Polyrhythms can be distinguished from irrational rhythms, which can occur within the context of a single part; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm. Concurrently in this context means within the same rhythmic cycle. The underlying pulse, whether explicit or implicit can be considered one of the concurrent rhythms. For example, the son clave is poly-rhythmic because its 3 section suggests a different meter from the pulse of the entire pattern.

In some European art music, polyrhythm periodically contradicts the prevailing meter. For example, in Mozart's opera Don Giovanni, two orchestras are heard playing together in different metres (³
₄ and ²
₄):

They are later joined by a third band, playing in ³
₈ time.

Polyrhythm is heard near the opening of Beethoven's Symphony No. 3. (See also syncopation.)

Chopin often explored the rhythmic possibilities inherent in the independence of a pianist's two hands. A spectacular example may be found in his Étude, Op, 10 No. 10. Alan Walker comments that while this piece is straightforward for listeners, "From the player’s point of view, however, nothing is straightforward. Chopin has placed him inside a veritable hornets’ nest of cross-rhythms and syncopations. The melody first emerges from a background of triplets, then of duplets. Accents are changed without warning, shifting the balance of the phrase sideways, so to speak, together with the place of each note within it."

Polyrhythm is a particularly common feature of the music of Brahms. Writing about the Violin Sonata in G major, Op. 78, Jan Swafford (1997, p. 456) says "In the first movement Brahms plays elaborate games with the phrasing, switching the stresses of the ⁶
₄ meter back and forth between 3+3 and 2+2+2, or superimposing both in violin and piano. These ideas gather at the climax at measure 235, with the layering of phrases making an effect that perhaps during the 19th century only Brahms could have conceived."

In "The Snow Is Dancing" from his Children's Corner suite, Debussy introduces a melody "on a static, repeated B-flat, cast in triplet-division cross rhythms which offset this stratum independently of the sixteenth notes comprising the two dancing-snowflake lines below it." "In this section great attention to the exactitude of rhythms is demanded by the polyrhythmic superposition of pedals, ostinato, and melody."

Concerning the use of a two-over-three (2:3) hemiola in Beethoven's String Quartet No. 6, Ernest Walker states, "The vigorously effective Scherzo is in ³
₄ time, but with a curiously persistent cross-rhythm that does its best to persuade us that it is really in ⁶
₈."