The problem of the stability of water-coated ice layer is investigated for a free surface flow down an inclined plane for the cases of normal and thin (boundary- layer scale) water films. For the case of boundary-layer scale water film a Froude- based double-deck theory is developed which is then used to investigate linear two-dimensional (2D), three-dimensional (3D) and nonlinear 2D stability of the problem. The new mode of upstream-propagating instability arising because of the ice layer is found and its properties investigated. In the linear double-deck, analytic expressions for the dispersion relation and neutral curves are obtained for the case of Pr = 1. For the general case, linear stability problem is solved numerically using new 4th order finite-difference scheme developed for Orr-Sommerfeld equations. Non-linear double-deck equations are solved with a new 2nd order in space global- marching type scheme and the effects of nonlinearity are analysed. An explanation of the physical mechanism leading to the upstream propagation is derived. The effect of the intersection and branch exchange between the interfacial mode and a shear mode is discovered in a 2-fluid plane Poiseuille flow and investigated in detail using linear stability theory and the numerical approach developed for the free-surface flows. The interaction between three instability modes present in the problem is analysed. It is shown that the question of mode identity becomes complicated because of the discovered intersection and the methods of establishing mode identity are discussed. Finally, the longwave asymptotic analysis of the ice layer under a water/air plane Poiseuille flow is performed. The effect of ice on the modes present in the problem is discussed
