  We develop a diagrammatic theory for transport of waves in disordered media
with weak nonlinearity. We first represent the solution of the nonlinear wave
equation as a nonlinear Born series. From this, we construct nonlinear ladder
and crossed diagrams for the average wave intensity. Then, we sum up the
diagrammatic series completely, i.e. nonperturbatively in the strength of the
nonlinearity, and thereby obtain integral equations describing both nonlinear
diffusive transport and coherent backscattering of the average intensity. As
main result, we find that the nonlinearity significantly influences the
magnitude of the coherent backscattering effect. Depending on the type of
nonlinearity, coherent backscattering is either enhanced or suppressed, as
compared to the linear case.
