  We investigate new compactifications of OM theory giving rise to a 3+1
dimensional open string theory with noncommutative $x^0$-$x^1$ and $x^2$-$x^3$
coordinates. The theory can be directly obtained by starting with a D3 brane
with parallel (near critical) electric and magnetic field components, in the
presence of a RR scalar field. The magnetic parameter permits to interpolate
continuously between the $x^0$-$x^1$ noncommutative open string theory and the
$x^2$-$x^3$ spatial noncommutative U(N) super Yang-Mills theory. We discuss
$SL(2,Z)$ transformations of this theory. Using the supergravity description of
the large $N$ limit, we also compute corrections to the quark-antiquark Coulomb
potential arising in the NCOS theory.
