  The two-loop anomalous dimension of the chiral matter superfields is
calculated for a general ${\cal N}=1$ supersymmetric gauge theory regularized
by higher covariant derivatives. We obtain both the anomalous dimension defined
in terms of the bare couplings, and the one defined in terms of the
renormalized couplings for an arbitrary renormalization prescription. For the
one-loop finite theories we find a simple relation between the higher
derivative regulators under which the anomalous dimension defined in terms of
the bare couplings vanishes in the considered approximation. In this case the
one-loop finite theory is also two-loop finite in the HD+MSL scheme. Using the
assumption that with the higher covariant derivative regularization the NSVZ
equation is satisfied for RGFs defined in terms of the bare couplings, we
construct the expression for the three-loop $\beta$-function. Again, the result
is written both for the $\beta$-function defined in terms of the bare couplings
and for the one defined in terms of the renormalized couplings for an arbitrary
renormalization prescription.
