In 1987 Miyaoka gave a criterion for the semistability of a vector bundle on a curve in terms of the numerical properties of a suitable divisor. In the last few years several generalizations of this criterion have appeared, dealing with bundles on higher dimensional projective varieties, Kaehler manifolds, principal bundles and Higgs bundles. In this talk I wish to present a version of Miyaoka’s criterion for principal Higgs bundles on complex projective manifolds, relating it to the semistability of the relevant bundles restricted to arbitrary curves and to their numerical properties.