  The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport
processes which are ballistic in a chosen `parallel' direction and diffusive
and all other `transverse' directions. The time-space transformations of this
Lie algebra and its infinite-dimensional extension, the
meta-Schr\"odinger-Virasoro algebra, are constructed. We also find the
representation suitable for non-stationary systems by proposing a generalised
form of the generator of time-translations. Co-variant two-point functions of
quasi-primary scaling operators are derived for both the stationary and the
non-stationary cases.
