  We investigate Schwinger-Dyson equations for correlators of Wilson line
operators in non-commutative gauge theories. We point out that, unlike what
happens for closed Wilson loops, the joining term survives in the planar
equations. This fact may be used to relate the correlator of an arbitrary
number of Wilson lines eventually to a set of {\it closed} Wilson loops,
obtained by joining the individual Wilson lines together by a series of
well-defined cutting and joining manipulations. For closed loops, we find that
the non-planar contributions do not have a smooth limit in the limit of
vanishing non-commutativity and hence the equations do not reduce to their
commutative counterparts. We use the Schwinger-Dyson equations to derive loop
equations for the correlators of Wilson observables. In the planar limit, this
gives us a {\it new} loop equation which relates the correlators of Wilson
lines to the expectation values of closed Wilson loops. We discuss perturbative
verification of the loop equation for the 2-point function in some detail. We
also suggest a possible connection between Wilson line based on an arbitrary
contour and the string field of closed string.
