We discuss various mechanisms for viscous dissipation in the linear response to oscillatory shear of incompressible foams (such as biliquid foams or dense emulsions). These include viscous flow of liquid in films and plateau borders; intrinsic viscosity of the surfactant layers; and diffusion resistance. Marangoni-type and marginal regeneration mechanisms are considered for the transport of surfactant. We predict (on the basis of typical parameters for biliquid foams) that the zero shear viscosity is usually dominated by the intrinsic dilational viscosity of the surfactant monolayers, though other forms of dissipation may be important in certain systems. We give a preliminary analysis of the frequency dependent rheology arising from an interplay between these dissipation processes and elastic storage mechanisms