  The twist three contributions to the $Q^2$-evolution of the spin-dependent
structure function $g_2(x_{Bj},Q^2)$ are considered in the non-local operator
product approach. Defining appropriate twist three distribution function we
derive their evolution equation for the nonsinglet case in leading order
approximation. In the limit $x_{Bj} \rightarrow 1$ as well as in the large
$N_c$ limit we confirm the result that the evolution of the nonsinglet part of
$g_2$ is governed by a Gribov-Lipatov-Altarelli-Parisi equation.
