Ever since the notion of fuzzy set was introduced by Zadeh¹² in 1965, the concept of fuzzy metric space was introduced by various authors in different directions. Especially, Deng¹, Erceg², Kaleva and Seikkala⁵, Karmosil and Michalek⁶ have introduced the concept of fuzzy metric space in different ways. George and Veeramani³ modified the concept of fuzzy metric spaces in the sense of Karmosil and Michalek⁶ and defined the Hausdorff topology of fuzzy metric spaces. Consequently they showed every metric induces a fuzzy metric. Mishra, Sharma and Singh⁹ also proved some fixed point theorems in fuzzy metric spaces. Sushil Sharma¹³ proved common fixed point theorems for six mappings. In this paper we define a generalized contractive condition for a self mapping with respect to another and establish the existence of coincidence point. Further we deduce a weak contractive condition for the existence of fixed point for single mapping. We begin with some definitions and preliminary concepts.