Let G = (V (G),E(G)) be a simple undirected graph of order n, and let S ⊆ V (G). If every vertex in V (G) − S is adjacent to at least one vertex in S, then the set S is called a dominating set. The domination number of G is the minimum cardinality taken over all sets of S, and it is denoted by (G). Recently, the effect of one or more edges deletion on the domination number has been examined in many papers. Let F ⊆ E(G). The bondage number b(G) of G is the minimum cardinality taken over all sets of F such that (G−F) > (G). In the literature, a lot of domination and bondage parameters have been defined depending on different properties. In this paper, we investigate the bondage, strong and weak bondage numbers of complementary prism graphs of some well-known graph families.