ABSTRACT A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by . We denote the cartesian product of G and H by . In this paper, we find the 2-dynamic chromatic number of cartesian product of complete graph with complete graph , complete graph with complete bipartite graph and wheel graph with complete graph .