Whistler waves propagating near the quasi-electrostatic limit can interact with energetic protons (~80--500 keV) that are transported into the radiation belts. The waves may be launched from either the ground or generated in the magnetosphere as a result of the resonant interactions with trapped electrons. The wave frequencies are significant fractions of the equatorial electron gyrofrequency, and they propagate obliquely to the geomagnetic field. A finite spectrum of waves compensates for the inhomogeneity of the geomagnetic field allowing the protons to stay in gyroresonance with the waves over long distances along magnetic field lines. The Fokker-Planck equation is integrated along the flux tube considering the contributions of multiple-resonance crossings. The quasi-linear diffusion coefficients in energy, cross energy/pitch angle, and pitch angle are obtained for second-order resonant interactions. They are shown to be proportional to the electric fields amplitudes. Numerical calculations for the second-order interactions show that diffusion dominates near the edge of the loss cone. For small pitch angles the largest diffusion coefficient is in energy, although the cross energy/pitch angle term is also important. This may explain the induced proton precipitation observed in active space experiments. ¿ American Geophysical Union 1994