  We consider stochastic differential equations (SDEs) driven by Feller
processes which are themselves solutions of multivariate Levy driven SDEs. The
solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the
process consisting of the driving process and the solution is Markov and even
Feller in the case of bounded coefficients. The generator as well as the
semimartingale characteristics of this process are calculated explicitly and
fine properties of the solution are derived via the stochastic symbol. A short
simulation study and an outlook in the direction of stochastic modeling round
out the paper.
