  We study the deformation (Moyal) quantisation of gravity in both the ADM and
the Ashtekar approach. It is shown, that both can be treated, but lead to
anomalies. The anomaly in the case of Ashtekar variables, however, is merely a
central extension of the constraint algebra, which can be ``lifted''.
  Finally we write down the equations defining physical states and comment on
their physical content. This is done by defining a loop representation. We find
a solution in terms of a Chern-Simons state, whose Wigner function then becomes
related to BF-theory. This state exist even in the absence of a cosmological
constant but only if certain extra conditions are imposed. Another solution is
found where the Wigner function is a Gaussian in the momenta.
  Some comments on ``quantum gravity'' in lower dimensions are also made.
