In [8] Lj. Ćirić proved the following theorem on coincidence point: Let $(X,d)$ be a metric space, $T\colon X\to CL(X)$ (the family of nonempty, closed subsets of $X$) and $I\colon X\to X$ such that $T(X)\subseteq I(X)$. If $I(X)$ is $(T,I)$ orbitally complete and for each $x,y\in X$ \begin{multline*} H(Tx,Ty)eq a\max\{d(Ix,Iy),d(Ix,Tx),d(Iy,Ty),frac12[d(Ix,Ty) d(Iy,Tx)]\}+b\min\{\max{d(Ix,Tx),d(Iy,Ty)},frac12[d(Ix,Ty)+d(Iy,Tx)]\} \end{multline*} where $a,b\in\mathbf R$, $a\geq 0$, $b>0$, $a+b=1$, then there exists $z\in X$ such that $Iz\in Tz$. In this paper we shall give a generalization of this theorem for a family of multivalued mappings $\{T_n\}_{n\in \mathbf N}$.