We solve the superradiant laser model in two limiting cases. First the stat
ionary low-pumping regime is considered where a first-order phase transitio
n in the semiclassical solution occurs. This discontinuity is smeared out i
n the quantum regime. Second, we solve the model in the non-stationary regi
me where we find a temporally periodic solution. For a certain parameter ra
nge well-separated pulses may occur.