本文描述於二度空間裡，前進在兩層流體中之週期性規則表面及界面重力波的問題。對波浪場中各物理量以攝動羃級數展開，將所有的控制方程式展開成系統化的公式，並逐階解析波動流場至第三階解。本文所得之三階近似解可滿足所有的控制方程式及邊界條件，解決了往昔學者如Umeyama (2002) 與Song (2004) 等所得之解無法滿足邊界條件的問題。最後，由此三階解可以描述在不同流體厚度比與不同流體密度下之界面波與以及其所衍生之表面波動變化情形。

This paper describes the third-order solution for the nonlinear internal and surface progressive water wave in a two-layer fluid. We use the perturbation method to develop a mathematical derivation. The third-order asymptotic solution which satisfies the governing equation and boundary conditions is constructed and analyses in detail. This overcomes the problem that the solutions derived by Umeyama (2002) and Song (2004) can not satisfy the boundary conditions. This solution enables to describe the features of the interface wave and induced surface wave.