  Let X be an irreducible smooth projective curve of genus at least two over an
algebraically closed field k of characteristic p>0. In this paper we study the
natural stratification, defined using the absolute Frobenius of X, on the
moduli space of vector bundles on X of suitable rank. In characteristic two we
provide a complete classification of rank two semi-stable vector bundles whose
Frobenius pull-back is not semi-stable. We also obtain fairly good information
about the strata of the Frobenius stratification, including the irreducibility
and the dimension of each non-empty Frobenius stratum. In particular we show
that the locus of Frobenius destabilized bundles has dimension 3g-4 in the
moduli space of semi-stable bundles of rank two. We also construct stable
bundles that are destabilized by Frobenius in the following situations:
characteristic p=2 and rank four, (2) characteristic p=rank=3, (3)
characteristic p=rank=5 and g at least three.
  We also explore (in any characteristic) the connection between Frobenius
destabilized bundles and (pre)-opers, this approach allows us to reinterpret
some of our results in terms of pre-opers and also allows us to construct
Frobenius destablised bundles from certain pre-opers (or opers).
  The other result we obtain is (for characteristic two): we show that the
Gunning bundle descends under Frobenius when genus g is even. If g is odd, then
the Gunning bundle twisted by any odd degree line bundle also descends.
