For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e∉G, there is a copy of F in G+e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n,F). A graph G is weakly F-saturated if G contains no copy of F and there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n,F). The graphs of order n that are weakly F-saturated will be denoted by wSAT(n,F), and those graphs in wSAT(n,F) with wsat(n,F) edges will be denoted by wSAT¯(n,F). The precise value of wsat(n,F) for many families of vertex disjoint copies of connected graphs such as small order graphs, trees, cycles, and complete graphs will be determined.