  Generalising and unifying the known theorems for difference and differential
fields, it is shown that for every finite free ${\mathbb S}$-algebra ${\mathcal
D}$ over a field $A$ of characteristic zero the theory of ${\mathcal D}$-fields
has a model companion ${\mathcal D}$-CF$_0$ which is simple and satisfies the
Zilber dichotomy for finite-dimensional minimal types.
