  We obtain the Penrose limit of six dimensional Non-Commutative Open String
(NCOS$_6$) theory and show that in the neighborhood of a particular null
geodesic it leads to an exactly solvable string theory (unlike their
counterparts in four or in other dimensions). We describe the phase structure
of this theory and discuss the Penrose limit in different phases including Open
D-string (OD1) theory. We compute the string spectrum and discuss their
relations with the states of various theories at different phases. We also
consider the case of general null geodesic for which the Penrose limit leads to
string theory in the time dependent pp-wave background and comment on the
renormalization group flow in the dual theory.
