  We analyze the d'Alembert equation in the Goedel-type spacetimes with
spherical and Lobachevsky sections (with sufficiently rapid rotation). By
separating the $t$ and $x_3$ dependence we reduce the problem to a
group-theoretical one. In the spherical case solutions have discrete
frequencies, and involve spin-weighted spherical harmonics. In the Lobachevsky
case we give simple formulas for obtaining all the solutions belonging to the
$D^\pm_\la$ sectors of the irreducible unitary representations of the reduced
Lorentz group. The wave equation enforces restrictions on $\la$ and the allowed
(here: continuous) spectrum of frequencies.
