The acoustic combustion instability of a solid fuel rocket depends vitally on the response of the burning propellant surface to a sound field. The erosive part of this response can be significantly nonlinear at sound amplitudes too low in typical motors for ordinary second-order acoustic nonlinearities to be important. Then moderate amplitude phenomena can be ascribed to erosive nonlinearities, and these can be isolated for analysis. This is done by examining the growth constants of the acoustic modes A previous paper has shown that nonlinear erosion can destabilize axial modes which are linearly stable or can limit linearly unstable ones to moderate amplitudes. That discussion is generalized here, and a unified summary of acoustic erosion contributions to stability is given. Other effects of nonlinear erosivity are then analyzed. It is shown that erosive generation of harmonics can produce considerable waveform distortion of moderate amplitude axial modes. Also, it is found that the nonlinear erosion mechanism can lead to severe oscillations, with consequent sharp mean pressure peaks, at rocket geometries where two acoustic modes are degenerate. This theory of nonlinear erosive interactions of a mode with itself, with its harmonics, and with degenerate modes seems to agree qualitatively with various experimental observations.