In this paper, the wave velocity c is developed as an asymptotic series forweak nonlinear waves in non-uniform flow. Then Fredholm’s alternative theoremis applied and it is verified that the first-order approximation c1 equals zero,This generalizes the previous result. In this paper, the wave velocity c is developed as an asymptotic series forweak nonlinear waves in non-uniform flow. Then Fredholm’s alternative theoremis applied and it is verified that the first-order approximation c1 equals zero, This generalizes the previous result.