An analytical study is presented for the solution of a generalizedGraetz problem in a right, annular, cylindrical tube of arbitrary cross-section, which contains a fully-developed, steady, unidirectional, multicomponent flow. The problem incorporates arbitrary inlet-conditions and considerably general, inhomogeneous boundary-conditions. Each component flow is characterized by a prescribed velocity distribution and is under the influence of an arbitrary heat source. The system of differential equations for the temperature distribution in each component is coupled through interface-conditions which involve finite thermal conductance. Through the use of a novel procedure, which appears to be more convenient mathematically than any possible alternative, infinite series expressions are derived for the temperature distribution in each and every component, and various alternative forms are noted. The general expressions, not available hitherto, contain the solutions of many specialGraetz problems of engineering significance. An illustrative example of a two-component flow in an annular, circular cylinder is included.