  The spin-dependent structure functions g_2 (x, Q^2) are investigated within
the framework of the chiral quark soliton model. It turns out that the twist-3
part of g_2 (x, Q^2) gives nonnegligible contributions to the total
distributions at the energy scale of Q^2 = 5 {GeV}^2 but mainly in the smaller
x region only, so that the corresponding third moments \int_0^1 x^2 \bar{g}_2
(x, Q^2) dx are pretty small for both of the proton and neutron in conformity
with the recent E155 data.
