Let X be a complex topological vector space and L(X) the set of all continuous linear operators on X. An operator T ∈ L(X) is supercyclic if there is x ∈ X such that; COrb(T, x) = {αT n x : α ∈ C, n ≥ 0}, is dense in X. In this paper, we extend this notion from a single operator T ∈ L(X) to a subset of operators Γ ⊆ L(X). We prove that most of related proprieties to supercyclicity in the case of a single operator T remains true for subset of operators Γ. This leads us to obtain some results for C-regularized groups of operators.