The k-power domination problem is to determine a minimum size vertex set S V (G) such that after setting X = N[S] and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of v are not yet in X till we get X = V (G). The least cardinality of such set is called the k-power domination number of G and is denoted by γp,k(G). If k = 0 and 1 then the problem is called domination and power domination problem respectively. In this paper, we discuss the 2-power domination problem and we compute 2-power domination number to be 2 for certain interconnection networks such as torus, twisted torus, and certain bipartite graphs. © 2015 Academic Publications, Ltd.