The collinear magnetic structure of n (n = 1,..., 6) monolayers (ML) of Fe films deposited on Co(111) substrate is investigated by ab initio density functional theory within a generalized gradient approximation. We have found that the ferromagnetic ground state exists only for one Fe monolayer. For higher thickness, a sequence of antiferromagnetic coupling with low magnetic moments in the inner layers of films is identified as ground state. (c) 2005 Elsevier B.V. All rights reserved.