Using Grad's thirteen-moment approximation based on the relaxation model for collisions, the effects of streaming viscous drag and heat conduction on electromagnetic and electroacoustic waves travelling in warm drifting electron plasma are studied. The general dispersion relations for these waves are deduced and particular cases of non-streaming transverse and longitudinal streaming plasma are discussed in detail. Expressions for the velocities of the relevant propagation modes are obtained and the latter are then identified from the limiting values of these velocities. From the study described in this paper, it is observed that the viscous and conductive properties of the plasma have negligible effect on the electromagnetic modes, but that these do affect the electroacoustic modes as does the drift velocity. The effect of thermal conductivity is rather striking since it produces a splitting of the electroacoustic waves into slow and fast modes.