Pulse propagation in maser‐type traveling‐wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady‐state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady‐state pulses depend only on the ratio of the linear loss and gain coefficients. Steady‐state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from afinitevalue to zero. Steady‐state pulses propogate at a velocity less than that of the small signal velocity in the medium.