  We discuss the positivity of the hadron density matrix in QCD. This basic
property is shown to be preserved by QCD evolution, provided the relation
$|\Delta P_{ij}(z)| \leq P_{ij}$ is valid for all kernels for $z < 1$, and the
usual "+" prescription is used. We comment on the positivity restrictions for
the choice of the NLO factorization scheme for the evolution of the
spin-dependent parton distributions.
