A procedure to evaluate the thermodynamic speed of sound in systems with any number of fluid phases is presented in this paper. Starting from the definition of speed of sound, the derivation of the procedure uses the conservation equations for volume, entropy, and number of moles of each component, the derivatives of several thermodynamic properties, and the solution of a system of linear equations. A computer algebra program was used to automatically derive and implement in computer the required expressions. The calculated thermodynamic speeds of sound reported in this paper are in very good agreement with results published recently, based on numerical derivatives, but show some discrepancies with earlier results available in the literature. (C) 2011 Elsevier B.V. All rights reserved.