The main purpose of this paper is to prove some new coincidence and common fixed point theorems for noncommuting generalized f-nonexpansive multivalued mappings on non-starshaped domain in the framework of a Banach space. As applications, related common fixed point, invariant approximation, and random coincidence point results are established. This work provides extension as well as substantial improvement of several results in the existing literature. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. Introduction an