Many classes of mechanical systems must now be designed with members possessing high stiffness-to-weight ratios and high strength-to-weight ratios in order to achieve superior performance characteristics. One of the philosophies proposed for addressing these classes of problems requires the articulating members to be fabricated with modern composite materials. While these materials enable high-strength, high-stiffness and low-mass members to be fabricated, the properties of these polymeric materials are adversely affected by elevated temperatures and also moisture absorption. The subject of this paper is the development of a methodology for predicting the dynamic hygrothermoelastic response of machine systems fabricated with these advanced materials. This methodology is based on a variational theorem which provides the basis for a finite element formulation. An illustrative example serves to demonstrate some preliminary work on predicting the response of a four-bar linkage fabricated with polymeric composite links simultaneously subjected to both mechanical and hygrothermal loadings.