We present an analysis of motion of charged test particles in a class
of Godel-type rotating spacetimes. The wave equation for a charged sca
lar field is solved and the allowed frequencies are computed. We show
that due to the presence of a background electromagnetic field unbound
ed trajectories may occur in these acausal spacetimes. The problem of
field quantization in the presence of closed timelike curves using the
Euclidean approach to quantum field theory is also considered.