The Quasi-Steady vaporization and combustion of a multicomponent, spherically symmetrical droplet composed of a thermodynamically ideal mixture of mutually soluble fuels is analyzed theoretically by approximating the discrete mixture by a Continuous Mixture (CM). The CM is described locally by a general Probability Density Function (PDF), which is approximated by a truncated spectral expansion with a number of 'components' much smaller than the number of chemical components in the original mixture. Two methods (Galerkin and Orthogonal Collocation OC) are proposed, discussed, and OC is used, to solve the evolution of the spectral governing equations. The present paper generalizes the methods employed in most earlier Continuous Mixture Theory (CMT) studies, in which the PDF describing the mixture is assumed to have a predetermined mathematical form. These methods are illustrated for the practical cases of vaporization and combustion of individual droplets of gasoline, diesel or aviation fuel JP4. The results show that in most cases our spectral OC provides useful results with as few as six spectral pseudocomponents. (C) 2003 The Combustion Institute. All rights reserved.