We analyze further the IR singularities that appear in noncommutative field
theories on R-d. We argue that all IR singularities in nonplanar one loop
diagrams may be interpreted as arising from the tree level exchanges of new
light degrees of freedom, one coupling to each relevant operator. These ex
changes are reminiscent of closed string exchanges in the double twist diag
rams in open string theory. Some of these degrees of freedom are required t
o have propagators that are inverse linear or logarithmic. We suggest that
these can be interpreted as free propagators in one or two extra dimensions
respectively. We also calculate some of the IR singular terms appearing at
two loops in noncommutative scalar field theories and find a complicated m
omentum dependence which is more difficult to interpret.