  We calculate the spin dependent structure functions g_{1}(x) and g_{2}(x) of
the proton and neutron. Our calculation uses the meson cloud model of nucleon
structure, which has previously given a good description of the HERMES data on
polarized sea quark distributions, and includes all the leading contributions
to spin dependent effects in this model. We find good agreement between our
calculations and the current experimental data for the structure functions. We
include in our calculations kinematic terms, which mix transverse and
longitudinal spin components, for hadrons of spin 1/2, 1 and 3/2, and which can
give considerable contributions to the g_{2} structure functions. We also
consider the possible interference terms between baryons or mesons in different
final states with the same quantum numbers, and show that most of these terms
do not give leading contributions to the spin dependent structure functions.
