The paper describes the study of the effect of oxidation on the magnetic coupling between Mn and Co atoms in ultrathin Mn films deposited on fee Co(001). The magnetic map has been investigated through tight-binding linear-muffin-tin scheme within generalized gradient approximation of the density functional. The calculations indicate that oxygen tends to destabilize the ferromagnetic Mn-Co coupling in favour of an antiferromagnetic coupling found by experiment when oxygen is added. Nevertheless, the (1 x 1) structures observed do not seem to be the most stable ones. We speculate that a disordered oxidized Mn-rich MnCo surface alloy might explain the experimental findings. (C) 2003 Elsevier B.V. All rights reserved.