  We investigate polarized deuteron structure functions at small values of the
Bjorken variable, x < 0.1. In this region contributions from the coherent
interaction of diffractively excited hadronic states with both nucleons become
important. A proper treatment of this process requires an extension of the
Glauber-Gribov multiple scattering theory to include spin degrees of freedom.
In the kinematic domain of current fixed target experiments we observe that
shadowing effects in g_1d are approximately twice as large as for the
unpolarized structure function F_2d. Furthermore at x < 0.1 the tensor
structure function b_1 is found to receive significant contributions from
coherent double scattering.
