For a graph G=(V,E), a sequence S=(v1,…,vk) of distinct vertices of G it is called a \emph{dominating sequence} if NG[vi]∖⋃j=1i−1N[vj]=∅. The maximum length of dominating sequences is denoted by γgr(G). We define the Grundy bondage numbers bgr(G) of a graph G to be the cardinality of a smallest set E of edges for which γgr(G−E)>γgr(G). In this paper the exact values of bgr(G) are determined for several classes of graphs