  I consider the problem of generalising the Abelian Coulomb gauge condition to
the non-Abelian Yang-Mills theory, with an arbitrary compact and semi-simple
gauge group. It is shown that a straightforward generalisation exists, which
reduces the Gauss law into a form involving the gauge potentials only, but not
their time derivatives. The existence and uniqueness of the generalised Coulomb
gauge is shown to depend on an elliptic linear partial differential equation
for a Lie-algebra valued quantity, which defines the gauge transform by means
of which the generalised Coulomb gauge condition is realised. Thus the Gribov
problem is actually non-existent in this case.
