- From Weinbergs nonlinear wave equation we derive the nonlinear generalization of the optical Bloch equations with radiative damping. We compare these equations with Fermis nonlinear radiation-reaction theory and with Jayness neoclassical theory. The nonlinear constant, which is small if compared to the binding energy per nucleon, can be comparable to the radiative lifetime of an excited state of an ion stored in an ion trap. We show that in such a case the nonlinear modification of the optical Bloch equations can lead to large-scale effects in coherent transients, in atomic quantum jumps, and in resonance fluorescence and can modify the emission line shape. 1990 The American Physical Society.