A reasonably complete theoretical description of stimulated scattering in the presence of low-reflectivity external feedback is presented, based on an earlier treatment by Lu and Harrison [Europhys. Lett. 16, 655 (1991)] generalized to account for the integral effect of nonlinear refraction. Theoretical results show the Stokes signal to exhibit huge sustained or random bursts of quasiperiodic emission. Detailed comparisons with experimental findings on stimulated Brillouin scattering generated in single-mode optical fiber with weak external feedback by continuous-wave excitation give good agreement regarding both the dynamical features of the Stokes emission and their dependence on the physical control parameters, e.g., pump power, cavity reflectivity, and fiber length. Significantly, our results confirm the essential role of nonlinear refraction to the dynamical behavior and suggest that the noise structure of the initial spontaneous scattering has little influence on this behavior. © 1992 The American Physical Society.