Most mechanisms can be assembled in two or more distinct configurations for a given position of the input link. Each distinct configuration is called a branch. When the prescribed positions of a synthesized mechanism lie on more than one branch, the mechanism is said to have branching problems or to suffer from “branch defect.” Usually, branching problems will render a mechanism unsuitable for the design task because the mechanism must be moved to the other branch during the course of motion. In most cases, this would require disassembly and reassembly of the mechanism. In this paper, conditions are developed for avoiding the branching problem in the spherical RRRR and spatial RCCC mechanisms. These conditions are ideally suited for incorporation into an optimization scheme as constraints because they do not require iterative calculations or a position analysis of the mechanism.