  Bloch oscillations appear for a particle in a weakly tilted periodic
potential. The intrinsic spin Hall effect is an outcome of a spin-orbit
coupling. We demonstrate that both these phenomena can be realized
simultaneously in a gas of weakly interacting ultracold atoms exposed to a
tilted optical lattice and to a set of spatially dependent light fields
inducing an effective spin-orbit coupling. It is found that both the spin Hall
as well as the Bloch oscillation effects may coexist, showing, however, a
strong correlation between the two. These correlations are manifested as a
transverse spin current oscillating in-phase with the Bloch oscillations.
