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This paper is concerned with the study of nonlinear stability ofsuperposition of boundary layer and rarefaction wave on the two-fluidNavier-Stokes-Poisson system in the half line $\mathbb{R}_{+}=:(0,+\infty)$. Onaccount of the quasineutral assumption and the absence of the electric fieldfor the large time behavior, we successfully construct the boundary layer andrarefaction wave, and then we give the rigorous proofs of the stabilitytheorems on the superposition of boundary layer and rarefaction wave undersmall perturbations for the corresponding initial boundary value problem of theNavier-Stokes-Poisson system, only provided the strength of boundary layer issmall while the strength of rarefaction wave can be arbitrarily large. Thecomplexity of nonlinear composite wave leads to many complicated terms in thecourse of establishing the {\it a priori} estimates. The proofs are given by anelementary $L^2$ energy method.

Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier-Stokes-Poisson system