  This paper is concerned with the study of nonlinear stability of
superposition of boundary layer and rarefaction wave on the two-fluid
Navier-Stokes-Poisson system in the half line $\mathbb{R}_{+}=:(0,+\infty)$. On
account of the quasineutral assumption and the absence of the electric field
for the large time behavior, we successfully construct the boundary layer and
rarefaction wave, and then we give the rigorous proofs of the stability
theorems on the superposition of boundary layer and rarefaction wave under
small perturbations for the corresponding initial boundary value problem of the
Navier-Stokes-Poisson system, only provided the strength of boundary layer is
small while the strength of rarefaction wave can be arbitrarily large. The
complexity of nonlinear composite wave leads to many complicated terms in the
course of establishing the {\it a priori} estimates. The proofs are given by an
elementary $L^2$ energy method.
