Summary: We prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes the theorems of

*K. Nakajo* and

*W. Takahashi* [J. Math. Anal. Appl. 279, No. 2, 372–379 (2003;

Zbl 1035.47048)]. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from the one of Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space.