The thermal stability of the exchange bias field H-E in samples of Cu (30 nm)/[ferromagnetic (FM) FeMn]/Cu (30 nm) and Cu (30 nm)/(FeMn/FM)/Cu (30 nm) prepared with an ultrahigh vacuum magnetron sputtering system was studied experimentally and by model calculations. The samples were heated to various temperatures and then kept for 10 min in an applied field of 1000 Oe antiparallel to the cooling field. It was found that H-E decreased when the annealing temperature was increased and became zero after annealing at about 100 degreesC. When the annealing temperature was further increased, H-E changed sign. Although the exchange bias field and the coercivity are strongly dependent on various factor, e.g., the stacking order of the layers, the thickness and the magnetization of FM layer, the thermal stability of the exchange bias field is influenced only by the thickness of antiferromagnetic (AFM) layer. A magnetic training effect appeared and became more apparent after annealing in a field antiparallel to the cooling field, especially for the samples with a thin AFM layer. (C) 2002 American Institute of Physics.