  We use Monte Carlo and Transfer Matrix methods in combination with
extrapolation schemes to determine the phase diagram of the 2D
super-antiferromagnetic (SAF) Ising model with next-nearest-neighbor (nnn)
interactions in a magnetic field. The interactions between nearest-neighbor
(nn) spins are ferromagnetic along x, and antiferromagnetic along y. We find
that for sufficiently low temperatures and fields, there exists a region
limited by a critical line of 2nd-order transitions separating a SAF phase from
a magnetically induced paramagnetic phase. We did not find any region with
either first-order transition or with re-entrant behavior. The nnn couplings
produce either an expansion or a contraction of the SAF phase. Expansion occurs
when the interactions are antiferromagnetic, and contraction when they are
ferromagnetic. There is a critical ratio R_c = 1/2 between nnn- and
nn-couplings, beyond which the SAF phase no longer exists.
