The stability of a two-fluid boundary layer is investigated. A boundary layer shears a second fluid that is bounded by the wall and the shearing fluid. The eigenvalue problem governing the linear stability of the configuration is solved using an efficient shooting-search method. Besides the Tollmien-Schlichting mode (hard mode) found in the classical hydrodynamical stability theory an additional Yih-mode (interfacial mode) exists due to the two-fluid interface. Effects of viscosity and density stratifications, thickness of the bounded fluid, gravity, surface tension as well as the non-Newtonian character of the lower fluid on the stability characteristics are determined. The interfacial mode is found to be very sensitive against viscosity stratification. However, with a highly viscous liquid layer, the system approaches a single-layer behavior. The shear-thinning non-Newtonian liquid layer is observed to have a stabilizing effect for both of the modes. Surface tension is stabilizing for shea waves for the interfacial mode but a more complex effect was observed for the hard mode. Gravity is stabilizing with a favorable density stratification. Density stratification alone is destabilizing for low and moderate values of this parameter but becomes stabilizing for higher values. When the external boundary layer profile is turbulent, the interfacial mode is more likely to be observed in an experiment. Agreement of the obtained results with experimental, theoretical and numerical results reported in the literature is good. This is encouraging as the study is intended for solving the stability characteristics of de/anti-icing fluid-air systems and comparing the results with the experimental data when they become available. (C) 1998 American Institute of Physics. [S1070-6631(98)01811-X].