It is shown that approximate fixed-point attractors rather than synchronized oscillations can be employed by a wide class of neural networks of oscillators to achieve an associative memory recall. This computational ability of oscillator neural networks is ensured by the fact that reduced dynamic equations for phase variables in general involve two terms that can be respectively responsible for the emergence of synchronization and cessation of oscillations. Thus the cessation occurs in memory retrieval if the corresponding term dominates in the dynamic equations. A bottomless feature of the energy function for such a system makes the retrieval states quasi-fixed points, which admit continual rotating motion to a small portion of oscillators, when an extensive number of memory patterns are embedded. An approximate theory based on the self-consistent signal-to-noise analysis enables one to study the equilibrium properties of the neural network of phase variables with the quasi-fixed-point attractors. As far as the memory retrieval by the quasi-fixed points is concerned, the equilibrium properties including the storage capacity of oscillator neural networks are proved to be similar to those of the Hopfield type neural networks.