Abstract
If artistic improvisation gives a predominant place to contingency, this contingency cannot be absolute, on pain of depriving improvisation of any technique. This article, by taking the case of dance improvisation, will explore the complex relationships between contingency and necessity, by analyzing how a relative contingency can arise from the external necessity of a given framework of action, and how an inner necessity can result from a contingency understood as a creative condition relative to the Kairos of a situation in the making. These two connections will ultimately be linked to two different approaches to the concept of emergence.