A macroscopic model of two-phase flow in packed beds, based on the volume-averaged equations of motion for the gas and liquid phases, was analyzed in an attempt to understand the onset and evolution of fully-developed pulsing flow in trickle beds. By assuming that solutions take the form of waves travelling at constant speed, periodic solutions to these equations are found which can be associated with long-time, asymptotic behavior of pulses in a very long bed. Families of one-dimensional waves which exist at a particular set of mass fluxes can be characterized by infinite period bifurcations in the travelling wave frame. We numerically follow these bifurcations as the fluxes are changed, generating bifurcation diagrams for the original model. The results predict that properties of one-dimensional pulses should correlate with the total superficial velocity through the bed. A hysteresis in the trickling-pulsing transition is also predicted.