Using an oscillatory network model that combines classical network models with phase dynamics, we demonstrate how the superposition catastrophe of pattern recognition may be avoided in the context of phase models. The model is designed to meet two requirements: on and off states should correspond, respectively, to high and low phase velocities, and patterns should be retrieved in coherent mode. Nonoverlapping patterns can be simultaneously active with mutually different phases. For overlapping patterns, competition can be used to reduce coherence to a subset of patterns. The model thereby solves the superposition problem.