  We review our previous studies of truncated Mellin moments of parton
distributions. We show in detail the derivation of the evolution equation for
double truncated moments. The obtained splitting function has the same rescaled
form as in a case of the single truncated moments. We apply the truncated
moments formalism to QCD analyses of the spin structure functions of the
nucleon, $g_1$ and $g_2$. We generalize the Wandzura-Wilczek relation in terms
of the truncated moments and find new sum rules. We derive the DGLAP-like
evolution equation for the twist-2 part of $g_2$ and solve it numerically. We
find also useful relations between the truncated and untruncated moments.
