Pt Mn ∕ Ni Fe exchange-biased bilayers have been grown epitaxially on Si (001) using molecular-beam epitaxy. Spontaneous formation of the chemically ordered face-centered-tetragonal phase of PtMn layer was confirmed without postgrowth magnetic-field annealing, whose Néel axis is perpendicular to the PtMn∕NiFe interface. The exchange anisotropy field stabilizes above a PtMn thickness of 15nm which is much lower than that for polycrystalline PtMn-based exchange-biased systems. For comparison, PtMn∕NiFe exchange-biased bilayers have been prepared epitaxially on MgO (001) substrate. Spontaneous formation of the chemically ordered PtMn layer was also confirmed with Néel axis parallel to the PtMn∕NiFe interface. The exchange anisotropy field of the bilayer on MgO stabilizes beyond a PtMn thickness of 15nm as well.