  In this paper, we establish the mathematical validity of the Prandtl boundary
layer theory for a class of nonlinear plane parallel flow of nonhomogeneous
incompressible Navier-Stokes equations. The convergence for the density and
velocity are shown under various Sobolev norms, including the physically
important space-time uniform norm, as well as the $L^\infty(H^1)$ norm. It is
mentioned that the mathematical validity of the Prandtl boundary layer theory
for nonlinear plane parallel flow is generalized to the nonhomogeneous case.
