The object of this theoretical investigation is to obtain a set of equations which will predict the behavior of a fluid as it changes phase. Irreversible thermodynamics is employed to obtain general rate equations which relate the fluxes and forces across the nonequilibrium region existing at a phase interface. Both plane and spherical interfaces are considered. Experimental means for determining the three transport coefficients which appear in the resulting equations are discussed. Approximate values for the transport coefficients are obtained from kinetic theory arguments. The present analysis is limited to phase-change problems which may be described by linear phenomenological equations; this is so when the change in the driving potentials is small as compared to their value on either side of the phase interface. This restriction is necessary since presently no general theory exists for nonlinear rate processes.