We establish some coincidence and common fixed point theorems for mappings satisfying a generalized $(\psi,\varphi)$-weakly contractive condition in complete Hausdorff generalized metric spaces. Our results generalize very recent results of C. Di Bari and P. Vetro [Common fixed points in generalized metric spaces, Appl. Math. Comput. 218 (2012), 7322--7325] and extend and generalize many existing results in the literature.