Coordination among cortical neurons is believed to be a key element in mediating many high-level cortical processes such as perception, attention, learning, and memory formation. Inferring the structure of the neural circuitry underlying this coordination is important to characterize the highly nonlinear, time-varying interactions between cortical neurons in the presence of complex stimuli. In this work, we investigate the applicability of dynamic Bayesian networks (DBNs) in inferring the effective connectivity between spiking cortical neurons from their observed spike trains. We demonstrate that DBNs can infer the underlying nonlinear and time-varying causal interactions between these neurons and can discriminate between mono- and polysynaptic links between them under certain constraints governing their putative connectivity. We analyzed conditionally Poisson spike train data mimicking spiking activity of cortical networks of small and moderately large size. The performance was assessed and compared to other methods under systematic variations of the network structure to mimic a wide range of responses typically observed in the cortex. Results demonstrate the utility of DBN in inferring the effective connectivity in cortical networks.