  Anisimov and Seifert show that a group has a regular word problem ifand only
if it is finite. Muller and Schupp (together with Dunwoody's accessibility
result) show that a group has context free word problem if and only if it is
virtually free. In this note, we exhibit a class of groups where the word
problem is as close as possible to being a context sensitive language. This
class includes the automatic groups and is closed under passing to finitely
generated subgroups. Consequently, it is quite large, including many groups
which are not finitely presented.
