We report simulations of the electrocorticogram of the cat and human, based on estimates of fibre range, fibre density, axonal and dendritic delays, and cortical synaptic density. The long-range cortical connections of real cortex were simplified to couplings of symmetric density, decreasing in density with range, on a closed (toroidal) surface. Non-specific cortical activation was modelled as a diffuse global input and specific sensory input as a localised white noise input. Spectral properties of output included peak densities at the frequencies of the major cerebral rhythms, a '1/f' spectral envelope and 'shift to the right' with increasing total power as non-specific activation increased. Steady-state travelling waves with a velocity of 5-7 m/s (human) and < 1 m/s (cat) were produced. Frequency/wavenumber analysis revealed an additional class of activity with wavenumbers independent of temporal frequency. All these findings accord qualitatively and quantitatively with existing physiological results. Global resonant modes were not prominent, but the simulations obey a restricted case of the analytical results of Nunez (1994). Wave/pulse relations resemble the findings of Freeman (1975).