A typical functional region in cortex contains thousands of neurons, therefore direct neuronal simulation of the dynamics of such a region necessarily involves massive computation. A recent efficient alternative formulation is in terms of kinetic equations that describe the collective activity of the whole population of similar neurons. A previous paper has shown that these equations produce results that agree well with detailed direct simulations. Here we illustrate the power of this new technique by applying it to the investigation of the effect of recurrent connections upon the dynamics of orientation tuning in the visual cortex. Our equations express the kinetic counterpart of the hypercolumn model from which Somers et al (Somers D, Nelson S and Sur M 1995 J. Neurosci. 15 5448-65) computed steady-state cortical responses to static stimuli by direct simulation. We confirm their static results. Our method presents the opportunity to simulate the data-intensive dynamical experiments of Ringach et al (Ringach D, Hawken M and Shapley R 1997 Nature 387 281-4), in which 60 randomly oriented stimuli were presented each second for 15 min, to gather adequate statistics of responses to multiple presentations. Without readjustment of the previously defined parameters. our simulations yield substantial agreement with the experimental results. Our calculations suggest that differences in the experimental dynamical responses of cells in different cortical layers originate from differences in their recurrent connections with other cells. Thus our method of efficient simulation furnishes a variety of information that is not available from experiment alone.