Let D be a − subalgebra of C− algebra A and  : D ! A be a linear operator. In this paper we introduce the notions of (approximately inner) − derivations and (approximately inner) − dynamics on C− algebras and present several results concerning on the approximately innerness of such dynamics. In particular we prove that if { t}t2R is a − dynamics on the C− algebra A satisfying k t k 2 k  k +1 and there exists a core D0 for the generator d of { t}t2R such that d (as a − derivation) is approximately inner on D0, then { t}t2R is an approximately inner − dynamics

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