  We study, in some detail, the linear stability of closed timelike curves in
the Goedel metric. We show that these curves are stable. We present a simple
extension (deformation) of the Goedel metric that contains a class of closed
timelike curves similar to the ones associated to the original Goedel metric.
This extension correspond to the addition of matter whose energy-momentum
tensor is analyzed. We find the conditions to have matter that satisfies the
usual energy conditions. We study the stability of closed timelike curves in
the presence of usual matter as well as in the presence of exotic matter
(matter that does satisfy the above mentioned conditions). We find that the
closed timelike curves in Goedel universe with or whithout the inclusion of
regular or exotic matter are also stable under linear perturbations. We also
find a sort of structural stability.
