  After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon
related to the topology of the bundle of gauge connections, we show that there
is a similar feature for noncommutative QED over Moyal space, despite the
structure group being Abelian, and we exhibit an infinite number of solutions
for the equation of Gribov copies. This is a genuine effect of noncommutative
geometry which disappears when the noncommutative parameter vanishes.
