  We discuss perturbative evolution of the polarized structure function g_1 in
the (x,Q^2) plane, with special regard to the small-x region. We determine g_1
in terms of polarized quark and gluon distributions using coefficient functions
to order alpha_s. At small x g_1 then displays substantial scale dependence,
which necessarily implies a corresponding scale dependence in the large-x
region. This scale dependence has significant consequences for the extraction
of the first moment from the experimental data, reducing its value while
increasing the error. Conversely, the scale dependence may be used to constrain
the size of the polarized gluon distribution.
