We investigate the propagation of pulses of spike activity in a neuronal network with feedforward couplings. The neurons are of the spike-response type with a firing probability that depends linearly on the membrane potential. After firing, neurons enter a phase of refractoriness. Spike packets are described in terms of the moments of the firing-time distribution so as to allow for an analytical treatment of the evolution of the spike packet as it propagates from one layer to the next. Analytical results and simulations show that depending on the synaptic coupling strength, a stable propagation of the packet with constant waveform is possible. Crucial for this observation is neither the existence of a firing threshold nor a sigmoidal gain function—both are absent in our model—but the refractory behavior of the neurons.