In this paper, a general common fixed point theorem for two pairs of subcompatible mappings satisfying integral type implicit relations is obtained in a metric space. Our result improves several results especially the result of Pathak et al. [6]. Also, another common fixed point theorem of Greguš type for four mappings satisfying a contractive condition of integral type in a metric space using the concept of subcompatibility is established which generalizes the result of Djoudi and Aliouche [1] and others. Again a third common fixed point theorem for two pairs of near-contractive subcompatible mappings is given which enlarges the result of Mbarki [5] and references therein.