Recent neurophysiological experiments using mammalian brains indicated that some cortical neurons exhibit oscillatory activities which can be of functional importance in visual perception. These findings suggest that the oscillation is an ubiquitous feature of cortical information processing carried out by columns which are receiving growing attention as functional subdivisions of cortical circuitry. On the assumption that a basic functional unit is a column comprising excitatory and inhibitory neurons, a network model of cortical memory processing which can account for these oscillations is proposed. Numerical simulations revealed that for appropriately determined parameters the network can attain memory-pattern retrieval resulting from fixed-point behaviour despite the fact that columns have the characteristic of oscillators.