This paper follows on The problems of density current. Part I. (1967), and consists of two chapters.
　In chapter 1, the stability problems of interfacial and internal waves are discussed.　At first the property of the wave-induced Reynolds stress at the Kelvin-Helmholtz　instability is examined. The present method is more general than in Part I. The result shows that the Reynolds stress in this case can be treated as a particular one of ordinary treatment of instability regulated by the second derivative of velocity profile of the general flow.
　Secondly the instability of interfacial wave at a two-layer flow is treated. The velocity profile of the upper layer is assumed parabolic. To solve the eigen value equation easily, a simplified method is used. Two numerical examples are recorded, and the results are agreeable. In the appendix the change of wave celerity of internal wave in a case, in which a mixed layer between two homogeneous layers exists, is examined.
　Thirdly the instability of internal wave with a shear flow is studied. The variation of fluid density is same as in the above-mentioned appendix. The result shows the noticeable effect of the velocity profile of shear flow in the upper homogeneous layer against the stability.
　In chapter 2, the problem of control section of two-layer flows is discussed. Firstly a case of the linear long wave is treated, and secondly the problem of interfacial hydraulic jump is examined. Thirdly the interfacial resistance and the variation of width of flow are taken into account. The sesult shows a new aspect of this problem, and it may be applicable to some actual events.