Fe/ Pt multilayers with modulation periods ⌳ = 24.1± 0.2 and 37.2± 0.1 Å and ͓110͔ ʈ ͓111͔ bcc-fcc texture were fabricated by magnetron sputtering on thermally oxidized Si wafers. The structural evolution of the multilayers with annealing temperature in the range of 300-600 K was studied by in situ x-ray diffraction ͑XRD͒ and x-ray reflectivity. Two temperature regimes were found from the XRD data. Below 534± 4 K slow, short-range diffusion is observed without significant broadening of the satellite peaks or changes in the texture. Above 534 K fast, long-range diffusion is observed accompanied by significant broadening of the satellites and rapid increase of the misorientations of the grains. The multilayers crystallize at about 583 K into the tetragonal FePt phase with a small degree of ordering and strong ͓111͔ texture. The transition resembles a first-order phase transition with a critical exponent  = 0.48± 0.01 which practically does not depend on ⌳. The bulk interdiffusion coefficient, determined from the decay of the −1 satellite of the ͑001͒ Bragg peak of the multilayers, can be expressed in Arrhenius form as D͑T͒ = ͑1.37± 0.26͒ ϫ 10 −6 exp͑−1.7± 0.6/ k B T͒ m 2 / s. The gradient-energy coefficient k, entering the Cahn-Hilliard diffusion equation ͓Acta Metallurg. 9, 795 ͑1961͒, 10, 179 ͑1962͒; J. Chem. Phys. 28, 258 ͑1959͔͒, was estimated from the ⌳ dependence of the diffusion coefficient to be ͑−6.8± 0.2͒ ϫ 10 7 eV/ cm.