Let \((X, d)\) be a complete metrically convex metric space, \(K\) a non-empty closed subset of \(X\), \(F, G: K \to CL(X), S, T\) selfmaps of \(K\). The hybrid contractions in this paper satisfy the inequality \(H(Fx, Gy) \leq \alpha d(Tx, Sy) + \beta[d(Tx, Fx) + d(Sy, Gy)] + \gamma[d(Tx, Gy) + d(Sy, Fx)]\) for each \(x,y \in X\), where \(\alpha, \beta, \gamma\) are nonnegative and satisfy the conditions \(\alpha + 2\beta + 2\gamma < 1\) and \((\alpha + \beta + \gamma)((1 + \beta + \gamma)/(1 - \beta - \gamma))^2 < 1\). The authors obtain sufficient conditions for the pairs \(F\) and \(T\) and \(G\) and \(S\) to have a coincidence. By adding some additional conditions, it is shown that the maps have a common fixed point. The results of this paper extend and correct similar results stated in \textit{A. Ahmad} and \textit{M. Imdad} [J. Math. Anal. Appl. 218, No.~2, 546-560 (1998; Zbl 0888.54046)] and \textit{A. Ahmed} and \textit{A. R. Khan} [ibid. 213, No. 1, 275-286 (1997; Zbl 0902.47047)].