  We examine the T-duality relation between 1+1 NCOS and the DLCQ limit of type
IIA string theory. We show that, as long as there is a compact dimension, one
can meaningfully define an `NCOS' limit of IIB/A string theory even in the
absence of D-branes (and even if there is no B-field). This yields a theory of
closed strings with strictly positive winding, which is T-dual to DLCQ IIA/B
without any D-branes. We call this the Type IIB/A Wound String Theory. The
existence of decoupled sectors can be seen directly from the energy spectrum,
and mirrors that of the DLCQ theory. It becomes clear then that all of the
different p+1 NCOS theories are simply different states of this single Wound
IIA/B theory which contain D-branes. We study some of the properties of this
theory. In particular, we show that upon toroidal compactification, Wound
string theory is U-dual to various Wrapped Brane theories which contain OM
theory and the ODp theories as special states.
