A number of problems on the development of surface and internal waves in fluids with complex rheophysical properties is solved in a linear formulation. The influence of the viscoelastic properties of non-Newtonian fluids and the dissipation properties and local deformation inertia of fluids with gas bubbles on the stability of such waves is investigated. The question of the stability of internal waves in a two-layered incompressible viscous fluid with a tangential velocity discontinuity has been studied in detail /1, 2/. It is known that a Kelvin-Helmholtz instability occurs in the short-wave domain while there is no instability in the long-wave domain because of the stabilizing action of stratification. However, waves with negative energies exist in this domain that become unstable in the presence of viscous dissipation. In this connection, investigation of the stability of waves with negative energies in two-layered non-Newtonian fluids characterized by more complex rheological behaviour is of interest.