: For a pair of integers 1F␥-r, the ␥-chromatic number of an r-uniform Ž .hypergraph Hs V, E is the minimal k, for which there exists a partition of V into subsets < <T , . . . , T such that elT F␥ for every egE. In this paper we determine the asymptotic1 k i Ž .behavior of the ␥-chromatic number of the random r-uniform hypergraph H n, p for allr