In this talk we consider the problem of testing the homogeneity/equality of covariance matrices under a complex elliptical model. The classic methods developed using a Gaussian model do not behave well when considering the large family of elliptical distributions and new approaches must be developed. We will consider the problem using the well known Generalized Likelihood Ratio Test and present the difficulties associated when the density generator function is not known or not well specified. Then we will present results obtained using the more restrictive distribution of Spherically Invariant Random Vectors associated with deterministic texture parameters. Finally, an application to a SAR change detection problematic will be discussed in order to illustrate the usefulness of the developed statistics.