  We formulate the canonical structure of Yang--Mills theory in terms of
Poisson brackets of gauge invariant observables analogous to Wilson loops. This
algebra is non--trivial and tractable in a light--cone formulation. For U(N)
gauge theories the result is a Lie algebra while for SU(N) gauge theories it is
a quadratic algebra. We also study the identities satsfied by the gauge
invariant observables. We suggest that the phase space of a Yang--Mills theory
is a co--adjoint orbit of our Poisson algebra; some partial results in this
direction are obtained.
