The evolution of the layer and crystallite structure of nanoscale Co/Cu multilayers was studied during annealing up to 740 degreesC. Two structural transformations were observed. Between 310 and 410 degreesC the initial [111] fibre texture altered into a [100] texture, accompanied by the growth of [100] crystallites. During annealing, the presence of strong coherency strains in the multilayer stacking was inferred from satellite reflection analysis. These strains are considered as a driving force for the texture change due to the elastic anisotropy of copper and fcc-cobalt. As a second transformation the decay of the multilayer stacking sets in above 470 degreesC and leads to the formation of a granular structure which predominates above 650 degreesC. Both structural alterations were observed during heating, whereas during cooling no further transformations occurred.