  We consider the existence of Einstein-Maxwell-dilaton plus fluid system for
the case of stationary cylindrically symmetric spacetimes. An exact
inhomogeneous $ \epsilon$-order solution is found, where the parameter
$\epsilon$ parametrizes the non-minimally coupled electromagnetic field. Some
its physical attributes are investigated and a connection with already known
G\"odel-type solution is given. It is shown that the found solution also
survives in the string-inspired charged gravity framework. We find that a
magnetic field has positive influence on the chronology violation unlike the
dilaton influence.
