A mixture consisting of n homogeneous phases having certain properties is considered. The geometry of the phase domains is arbitrary and the mixture as a whole is considered to be statistically homogeneous but generally anisotropic. Ideal conditions of thermal contact (a continuous temperature and thermal flux) at the phase boundary are assumed. A variational method is used to find both the upper and lower bounds of the effective thermal-conductivity coefficients of the mixture for given concentrations and the thermal-conductivity coefficients of the individual phases.