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 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, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time causing possible superluminality.