The general solution to the Bloch equation in the rotating frame which includes the effects of relaxation during a constant amplitude, off-resonance rf field has been developed. The solution is used to monitor the transient approach to steady-state saturation levels during off-resonance irradiation applied continuously or in pulses to systems with arbitrary relaxation rates. The time course of the magnetization during amplitude modulated rf pulses is followed with the general solution and the transverse relaxation time dependence of typical slice profiles is examined. The calculations serve to illustrate the generality of the solution. A thorough discussion of various computational concerns is provided.