  A time and space inhomogeneous Markov process is a Feller evolution process,
if the corresponding evolution system on the continuous functions vanishing at
infinity is strongly continuous. We discuss generators of such systems and show
that under mild conditions on the generators a Feller evolution can be
approximated by Markov chains with L\'evy increments.
  The result is based on the approximation of the time homogeneous space-time
process corresponding to a Feller evolution process. In particular, we show
that a $d$-dimensional Feller evolution corresponds to a $d+1$-dimensional
Feller process. It is remarkable that, in general, this Feller process has a
generator with discontinuous symbol.
