  The spin-dependent structure function of the deuteron, g_1D, is calculated
within a covariant framework. The off-shell structure of the bound nucleon
gives corrections to the convolution model at a level of half a percent for x
below 0.7, increasing to more than five percent at larger x. Overall, the
dominant source of error comes from the lack of knowledge associated with the
deuteron D-state, which may introduce an uncertainty in the neutron spin
structure function, g_1n, extracted from deuterium data of up to ten percent
for x around 0.2.
