The purpose of this paper is to introduce and study some sequence spaces which axe defined by combining the concepts of a sequence of Orlicz functions, invariant mean and lacunary convergence. We also examine some topological properties of these sequence spaces and establish some elemantary connections between them. These axe generalizations of those defined and studied by Savs and Rhoades [22] and Bataineh and Azar [2] and some others before
