We studied the propagation of paroxysmal discharges in disinhibited neocortical slices by developing and analyzing a model of excitatory regular-spiking neocortical cells with spatially decaying synaptic efficacies and by field potential recording in rat slices. Evoked discharges may propagate both in the model and in the experiment. The model discharge propagates as a traveling pulse with constant velocity and shape. The discharge shape is determined by an interplay between the synaptic driving force and the neuron's intrinsic currents, in particular the slow potassium current. In the model, N-methyl-D-aspartate (NMDA) conductance contributes much less to the discharge velocity than amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) conductance. Blocking NMDA receptors experimentally with 2-amino-5-phosphonovaleric acid (APV) has no significant effect on the discharge velocity. In both model and experiments, propagation occurs for AMPA synaptic coupling gAMPA above a certain threshold, at which the velocity is finite (non-zero). The discharge velocity grows linearly with the gAMPA for gAMPA much above the threshold. In the experiments, blocking AMPA receptors gradually by increasing concentrations of 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) in the perfusing solution results in a gradual reduction of the discharge velocity until propagation stops altogether, thus confirming the model prediction. When discharges are terminated in the model by the slow potassium current, a network with the same parameter set may display discharges with several forms, which have different velocities and numbers of spikes; initial conditions select the exhibited pattern. When the discharge is also terminated by strong synaptic depression, there is only one discharge form for a particular parameter set; the velocity grows continuously with increased synaptic conductances. No indication for more than one discharge velocity was observed experimentally. If the AMPA decay rate increases while the maximal excitatory postsynaptic conductance (EPSC) a cell receives is kept fixed, the velocity increases by approximately 20% until it reaches a saturated value. Therefore the discharge velocity is determined mainly by the cells' integration time of input EPSCs. We conclude, on the basis of both the experiments and the model, that the total amount of excitatory conductance a typical cell receives in a control slice exhibiting paroxysmal discharges is only approximately 5 times larger than the excitatory conductance needed for raising the potential of a resting cell above its action potential threshold.