We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory neurons. Each neuron is represented by the integrate-and-fire model, and is allowed to fire only one spike. Two types of propagating pulses are observed. During fast pulses, inhibitory neurons fire a short time before or after the excitatory neurons. During slow pulses, inhibitory cells fire well before neighboring excitatory cells, and potentials of excitatory cells become negative and then positive before they fire. There is a bistable parameter regime in which both fast and slow pulses can propagate. Fast pulses can propagate at low levels of inhibition, are affected by fast excitation but are almost unaffected by slow excitation, and are easily elicited by stimulating groups of neurons. In contrast, slow pulses can propagate at intermediate levels of inhibition, and are difficult to evoke. They can propagate without slow excitation, but slow excitation makes their propagation substantially more robust. Fast pulses can propagate in a wider parameter regime if inhibition decays slowly with time, whereas slow pulses can propagate in a wider parameter regime if the passive time constant of inhibitory cells is large. Strong inhibitory-to-inhibitory conductance eliminates the slow pulses and converts the fast traveling pulses into irregular pulses, in which the inhibitory neurons segregate into two groups that have different firing delays with respect to their neighboring excitatory cells. In general, the velocity of the fast pulse increases with the axonal conductance velocity c, but there are cases in which it decreases with c. We suggest that the fast and slow pulses observed in our model correspond to the fast and slow propagating activity observed in experiments on neocortical slices.