  In this paper we consider the local X-ray transform for general flows. We
extend the results on the local and global invertibility of the geodesic ray
transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a
general flow. The key improvement is that our argument for the ellipticity of
the conjugated operator $A_F$ (which is defined in Section 2) can be applied to
flows other than the geodesic flow.
