In this paper, we introduce and study the diskcyclicity and disk transitivity of a set of operators. We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity. As applications, we study the diskcyclicty of C0-semigroups and C-regularized groups. We show that a diskcyclic C0-semigroup exists on a complex topological vector space X if and only if dim(X ) = 1 or dim(X ) = ∞ and we prove that diskcyclicity and disk transitivity of C0-semigroups (resp C-regularized groups) are equivalent.