In theories of the dynamical behavior of continua, there are several ways of describing the dissipative effects which, in addition to heat conduction, accompany deformation. The oldest way is to employ a viscous stress which depends on the rate of strain, as is done in the theory of Navier-Stokes fluids. In another description of dissipation, one postulates the existence of internal state variables which influence the stress and obey differential equations in which the strain appears. A third approach is to assume that the entire past history of the strain influences the stress in a manner compatible with a general postulate of smoothness or" principle of fading memory". Experience in high-polymer physics shows that the mechanical behavior of many materials, including polymer melts and solutions, as well as amorphous, cross-linked solids and semi-crystalline plastics, is more easily described within the theory of materials with fading memory than by theories of the viscous-stress type, which do not account for gradual stress-relaxation, or by theories which rest on a finite number of internal state variables and which, therefore, give rise to discrete relaxation spectra when linearized.