The rate equations for a travelling-wave model of an axial-field N2 UV-laser are solved numerically including the limiting case of saturation. It is assumed that collisional coupling of the rotational levels is negligible. Thus the laser pulses are computed by superposing the pulses emitted by the different rotational transitions. The computed and measured laser pulses are compared and the pulse timing and shape are satisfactorily predicted. A discrepancy between calculated and measured pulse power arises from uncertainties in the excitation cross-sections for electron impact excitation, in the electron energy distribution and in spurious feedback of the laser pulses. The difference in emission from the two ends of the laser is very sensitive to feedback. Strong variations in population inversion and photon density along the laser tube are predicted. The calculations show that only a part of the gas volume radiates near saturation condition.