Let $${F_1, F_2, \ldots, F_k}$$ F 1 , F 2 , … , F k be graphs with the same vertex set V. A subset $${S \subseteq V}$$ S ⊆ V is a simultaneous dominating set if for every i, 1 ≤ i ≤ k, every vertex of F i not in S is adjacent to a vertex in S in F i ; that is, the set S is simultaneously a dominating set in each graph F i . The cardinality of a smallest such set is the simultaneous domination number. We present general upper bounds on the simultaneous domination number. We investigate bounds in special cases, including the cases when the factors, F i , are r-regular or the disjoint union of copies of K r . Further we study the case when each factor is a cycle.