  We study the Bloch and the little Bloch spaces of harmonic functions on the
real hyperbolic ball. We show that the Bergman projections from
$L^\infty(\mathbb B)$ to $\mathcal B$, and from $C_0(\mathbb B)$ to $\mathcal
B_0$ are onto. We verify that the dual space of the hyperbolic harmonic Bergman
space $\mathcal B^1_\alpha$ is $\mathcal B$ and its predual is $\mathcal B_0$.
Finally, we obtain an atomic decomposition of Bloch functions as a series of
Bergman reproducing kernels.
