Summary: We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani by using the new property and give some examples. Our results improve and generalize the main results of D. Mihet
in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 7, 2184–2188 (2010; Zbl 1195.54082
)] and many fixed point theorems in fuzzy metric spaces.