Abstract Following the experimental work of Groudeva-Zotova et al. [S. Groudeva-Zotova, D. Elefant, R. Kaltofen, D. Tietjen, J. Thomas, V. Hoffmann, C.M. Schneider, J. Magn. Magn. Mater. 263 (2003) 57] where the magnetic and structural characteristics of a bi-layer NiMn–Co exchange biasing systems was investigated, density functional calculations with generalized gradient corrections were performed on (Mn 0.5Ni 0.5) n ordered alloy on Co(0 0 1) and one Mn 1− x Ni x monolayer on Co(1 1 1). For the Mn 0.5Ni 0.5 monolayer on Co(0 0 1), magnetic moments per surface atom of 0.65 μ B and 3.76 μ B were obtained for Ni and Mn, respectively. Those magnetic moments are aligned parallel to the total moment of Co(0 0 1). A complex behavior of the Mn moment in dependence of the thickness “ n” is obtained for (Mn 0.5Ni 0.5) n on Co(0 0 1). Investigations on Mn 1− x Ni x monolayer on Co(1 1 1) have shown that the crystallographic orientation does not modify significantly neither the magnetic moments of Mn and Ni atoms nor their ferromagnetic coupling with the Co(1 1 1) substrate, except for x = 0.66. For x = 0.66 the Mn sub-lattice presents an antiferromagnetic coupling leading to a quenching of the Ni magnetic moment.