We discuss various mechanisms for viscous dissipation in the linear re
sponse to oscillatory shear of incompressible foams (such as biliquid
foams or dense emulsions). These include viscous flow of liquid in fil
ms and plateau borders; intrinsic viscosity of the surfactant layers;
and diffusion resistance. Marangoni-type and marginal regeneration mec
hanisms are considered for the transport of surfactant. We predict (on
the basis of typical parameters for biliquid foams) that the zero she
ar viscosity is usually dominated by the intrinsic dilational viscosit
y 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.