  We perform a perturbative ${\cal O}(g^4)$ Wilson loop calculation for the
U(N) Yang-Mills theory defined on non-commutative one space - one time
dimensions. We choose the light-cone gauge and compare the results obtained
when using the Wu-Mandelstam-Leibbrandt ($WML$) and the Cauchy principal value
($PV$) prescription for the vector propagator. In the $WML$ case the
$\theta$-dependent term is well-defined and regular in the limit $\theta \to
0$, where the commutative theory is recovered; it provides a non-trivial
example of a consistent calculation when non-commutativity involves the time
variable. In the $PV$ case, unexpectedly, the result differs from the $WML$ one
only by the addition of two singular terms with a trivial $\theta$-dependence.
We find this feature intriguing, when remembering that, in ordinary theories on
compact manifolds, the difference between the two cases can be traced back to
the contribution of topological excitations.
