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 bot
h nucleons become important. A proper treatment of this process requir
es an extension of the Glauber-Gribov multiple-scattering theory to in
clude spin degrees of freedom. In the kinematic domain of current fixe
d target experiments we observe that shadowing effects in g(1)(d) are
approximately twice as large as for the unpolarized structure function
F-2(d). Furthermore at x<0.1 the tensor structure function b(1) is fo
und to receive significant contributions from coherent double scatteri
ng.