In Crisp environment, the notion of cyclic group on a set is well known. We study an extension of this classical notion to the Mfuzzy sets to define the concept of Mcyclic fuzzy groups. By using these cyclic ,M-fuzzy groups, we then define cyclic M-fuzzy group family and investigate its structure properties with applications. 2000AMS Subject classification: 08A72 , 20N25, 03E72, 94D05