The coupled-mode equations are solved for homogeneously broadened lasers modulated near the axial mode separation frequency. The character of the oscillations changes rapidly when the modulation period is tuned through the round-trip delay at the group velocity. Specifically, this is the region in which phase modulation leads to pulsing and loss modulation leads to pulsing at normal power. The present method agrees with the results of Kuizenga and Siegman for this region, but gives a countable set of supermodes in addition. There is some reason to believe that these other modes have already been observed. When the group velocity condition is not satisfied, a more complete description is given than has been previously reported. Most importantly, the dependence of laser power on modulator drive and frequency can be predicted.