Doi and Edwards have recently proposed a molecular theory for the dynamics of entangled polymer liquids based on a tube model to represent the mutual constraints on configurational rearrangement of the chains. Expressions for diffusion coefficient, plateau modulus, zero-shear viscosity, steady-state recoverable compliance, and terminal relaxation time can be devloped, and relations among these properties that depend only upon observable quantities can be obtained. Several such relations are derived and are compared with experimental observations.