  Following a previous study of the one-loop factorization of the nonsinglet
$g_2$ structure function of the nucleon, we present in this paper the
next-to-leading order coefficient functions in the singlet sector. To obtain
the result, the partonic processes of virtual Compton scattering off two and
three "on-shell" gluons are calculated. A key step in achieving the correct
factorization is to separate the correct twist-two contribution. The
Burkardt-Cottingham sum rule is nominally satisfied at this order.
