  I consider Higgs bundles satisfying a notion of ampleness that was introduce
Bruzzo, Gra\~na Otero and Hern\'andez Ruip\'erez, and prove that the Chern
classes of rank $r$ H-ample Higgs bundles over dimension $n$, polarized,
smooth, complex, projective varieties are positive under opportune hypothesis.
I extend this to non-negativeness of Chern classes of all numerically effective
Higgs bundles; and use this condition to prove the vanishing of Chern classes
of numerically flat Higgs bundles.
