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Abstract: Based on the three-dimensional effective Luttinger Hamiltonian and the exact Heisenberg equations of motion and within a self-consistent semiclassical approximation, we present a theoretical investigation on the nontrivial ac spin responses due to the intrinsic spin–orbit coupling of holes in p-doped bulk semiconductors. We show that the nontrivial ac spin responses induced by the combined action of an ac external electric field and the intrinsic spin–orbit coupling of holes may lead to the generation of a nonvanishing ac spin Hall current in a p-doped bulk semiconductor, which shares some similarities with the dissipationless dc spin Hall current conceived previously and also exhibits some interesting new features that was not found before. [Copyright &y& Elsevier]