  Let $\calM=\Gamma\bs \calH^{(n)}$, where $\calH^{(n)}$ is a product of $n+1$
hyperbolic planes and $\Gamma\subset\PSL(2,\bbR)^{n+1}$ is an irreducible
cocompact lattice. We consider closed geodesics on $\calM$ that propagate
locally only in one factor. We show that, as the length tends to infinity, the
holonomy rotations attached to these geodesics become equidistributed in
$\PSO(2)^n$ with respect to a certain measure. For the special case of lattices
derived from quaternion algebras, we can give another interpretation of the
holonomy angles under which this measure arises naturally.
