The nonlinear effects in weakly turbulent plasmas in the region of particle‐wave resonance are shown to be derivable by determining the response of the plasma to an infinitesimal test wave. The local solutions of the test‐wave responses are examined and the smearing of the particle‐wave resonances and the resulting change in the dispersion relation for the gentle bump instability are determined. The lowest‐order nonlinear transport equation is derived and applied to a weak homogeneous beam.