We consider a string-inspired, gravitational theory of scalar and electroma
gnetic fields and eve investigate the existence of axially symmetric, Godel
-type cosmological solutions. The neutral ease is studied first and an "ext
reme" Godel-type rotating solution, which respects the causality, is determ
ined. The charged case is considered next and two new configurations, minim
ally coupled to gravity, are presented, for the electromagnetic field. Anot
her configuration motivated by the expected distribution of currents and ch
arges in a rotating universe is studied and shown to lead to a Godel-type s
olution for a space-dependent coupling function. Finally, we investigate th
e existence of Godel-type cosmological solutions in the framework of the on
e-loop corrected superstring effective action and we determine the sole con
figuration of the electromagnetic field that leads to such a solution. It t
urns out that, in all the charged cases considered, closed timelike curves
do appear and the causality is always violated. [S0556-2821(99)06920-9].