We study a biologically plausible but computationally simplified integrate-and-fire neuronal model. Oscillatory activity is analyzed in the networks with and without self-connections. We perform a detailed scan of four major parameters that represent the properties of neurons and synapses: connection ratio, connection strengths, post-synaptic potential decay rate and soma’s potential decay rate. It is observed that networks with different properties exhibit different periods and different patterns of synchrony. We find that generally these oscillations are robust against changes of parameters, meanwhile we also locate the parametric oundaries where oscillations break down.