In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy-2 metric space and fuzzy-3 metric space prove some common fixed point theorems for mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy-2 metric space and fuzzy-3 metric space. Our results extend, generalize and improve the corresponding results given by many authors. Keywords: Fuzzy metric space, Fuzzy 2-metric space, fuzzy-3 metric space ,Compatible mappings, Common fixed point
