  The Fatou-Julia iteration theory of rational functions has been extended to
quasiregular mappings in higher dimension by various authors. The purpose of
this paper is an analogous extension of the iteration theory of transcendental
entire functions. Here the Julia set is defined as the set of all points such
that complement of the forward orbit of any neighbourhood has capacity zero. It
is shown that for maps which are not of polynomial type the Julia set is
non-empty and has many properties of the classical Julia set of transcendental
entire functions.
