  In this paper I discuss whether superluminal particles exist in the general
relativistic theory of gravity. It seems that the answer to this question is
negative. In truth the result may only represent a difficulty to {\bf special}
but not general relativity, the later allowing both Lorentzian and Euclidian
metrics. An Euclidian metric does not restrict speed. Although only the
Lorentzian metric is stable \cite{Yahaloma}, an Euclidian metric can be created
under special gravitational circumstances and persist in a limited region of
space-time causing possible superluminality.
