Fe͑110͒ nanostripe arrays, consisting of alternating monolayer and double layer stripes, have been grown by step flow on vicinal W͑110͒ substrates. The magnetic easy axis switches from in-plane in the monolayer to perpendicular in the double layer stripes. The data strongly suggest that magnetostatic interactions induce antiferromagnetic order in the double layer nanostripe array. It can be switched into a ferromagnetic arrangement by low external fields.The progress in the field of epitaxial magnetic films, including the discovery of indirect exchange coupling 1-3 and giant magnetoresistance ͑GMR͒, 4,5 is based on techniques to control perpendicular profiles-both of composition and of magnetic properties-on a nanoscale. Recently, there has been increased interest in extending those concepts from perpendicular to lateral magnetic nanostructures-that means to two-dimensional arrays of magnetic nanowires or nanostripes-prepared either by lithographic techniques 6 or by self-organization on grooved 7,8 or on vicinal single crystal substrates. 9-11 A promising candidate for pronounced magnetoresistance would be given by a film containing an array of antiferromagnetically coupled magnetic nanowires, which could be switched from antiferromagnetic towards ferromagnetic order by low magnetic fields. For the case of perpendicularly magnetized nanowires, the antiferromagnetic coupling would be provided by magnetostatic interaction. The aim of the present letter is to show that arrays of pseudomorphic double-layer ͑DL͒ nanostripes of Fe͑110͒ on W͑110͒, prepared on vicinal W͑110͒ substrates, present just this type of magnetic order. The DL stripe system then resembles a system of magnetic stripe domains in a homogeneous film of perpendicular anisotropy, which has been used recently as as giant magnetoresistance medium. 12 However, contrary to the 200 nm period in the stripe domain system, which is of pure magnetic origin, the magnetic ordering period in our samples is morphologically defined, and dramatically reduced to 18 nm only.Our work is based on a previous experimental study of monolayer ͑ML͒ nanostripes of Fe͑110͒, prepared on vicinal W͑110͒ surfaces. 11 Their magnetic properties are dominated by a strong uniaxial magnetic anisotropy with an easy axis in the plane, but across the stripe axis, resulting in ferromagnetic interstripe coupling of magnetostatic origin, and in dipolar superferromagnetism. In the present letter, we focus on pseudomorphic Fe͑110͒ nanostripes prepared on vicinal W͑110͒ in the range between one and two pseudomorphic atomic layers ͑ALs͒. In this range, puzzling magnetic phenomena have been observed before for the case of films pre-pared on smooth W͑110͒, which consisted of DL islands in a ML sea. Frustration of remanent magnetic order in the center of this range, 13 explained in terms of a quasiantiferromagnetic interaction of unknown origin between DL islands, was alternatively interpreted in terms of magnetic freezing. 14,15 Only recently it could be shown that the origin of this frustration i...