This paper deals with mixtures of nonisotropic media. The mixing formulas to describe the effective material parameters of the mixture are complicated expressions where the different parameter dyadics are coupled. Using six-vector notation, the different mixing rules become more manageable. However, for certain effective theories the matrix equations have been tractable only through numerical approach. Here we present a way to solve the effective material parameters in closed form, using an approach where the eigenvectors of the material six matrix are exploited. As a numerical example, the effective parameters of a mixture are calculated where the inclusion material is a mirror image of the background medium. ¿ American Geophysical Union 1996