Emergence of synchronous oscillatory activity is an inherent feature of the olfactory systems of insects, mollusks and mammals. A class of simple computational models of the mammalian olfactory system consisting of olfactory bulb and olfactory cortex is constructed to explore possible roles of the related neural circuitry in olfactory information processing via synchronous oscillations. In the models, the bulbar neural circuitry is represented by a chain of oscillators and that of cortex is analogous to an associative memory network with horizontal synaptic connections. The models incorporate the backprojection from cortical units to the bulbar oscillators in particular ways. They exhibit rapid and robust synchronous oscillations in the presence of odorant stimuli, while they show either nonoscillatory states or propagating waves in the absence of stimuli, depending on the values of model parameters. In both models, the backprojection is shown to enhance the establishment of large-scale synchrony. The results suggest that the modulation of neural activity through centrifugal inputs may play an important role at the early stage of cortical information processing.