  For certain classes of negative definite symbols $q(x,\xi)$ and state space
dependent Bernstein function $f(x,s)$ we prove that $-p(x,D)$, the
pseudo-differential operator with symbol $-p(x,\xi)=-f(x,q(x,\xi))$, extends to
the generator of a Feller semigroup. Our result extends previously known
results related to operators of variable (fractional) order of differentiation,
or variable order fractional powers. New concrete examples are given.
