Let X be a Banach space, K a nonempty closed subset of X and let T, S : K → X be two nonself almost contractions. In this paper, we prove the existence of coincidence points and common fixed points of almost contractions T and S. The main result shows that if S(K) is closed, the pair (T, S) has property (M′) and T and S satisfy some suitable conditions, then T and S have a unique common fixed point in K. This theorem generalizes several fixed point theorems for nonself mappings and also extend many great results in the fixed point theory of self mappings to the case on nonself mappings. Also, we give an example to support the validity of our results.