The problem analyzed in this paper is a specific application of the composite membrane. General diffusion and convection formulation is presented for the dynamic problem. The spectral analysis considers convective transport of a single solute species across a one dimensional membrane system. The solution is obtained using operator theoretic methods. The geometrical structure of the spectrum of the operator is determined for the complete range of the various parameters including the distribution coefficient, the convective velocity and the diffusion coefficient. The structure of the spectrum allows a complete characterization of all the eigenvalues of the system in terms of all of these physical parameters. Calculation of the first eigenvalue for a number of cases shows its variation with the convective velocity for various medium porosities and allows a priori estimates of the profiles.