  This paper discusses iterated monodromy groups for transcendental functions.
We show that for every post-singularly finite entire transcendental function,
the iterated monodromy action can be described by bounded activity automata of
a special form, called "dendroid automata". In particular, we conclude that the
iterated monodromy group of a post-singularly finite entire function is
amenable if and only if the monodromy group is.
