The subject of the present investigation is the influence of annealing on the microstructure of Co thin films. In particular, the evolution of the texture during annealing is studied and compared with that of Co/Cu multilayers of different individual layer thicknesses. 400nm thick Co films show a h.c.p. structure with a weak preference of the <001> texture component and a broad distribution of grain orientations. Annealing at about 350°C results in a strong increase of the h.c.p. <001> component, nearly complete disappearance of the statistical distribution and grain growth of a minor f.c.c. fraction in the films. In-situ XRD measurements on single Co films during annealing confirm that the texture change is irreversible. Multilayer stacks of Co/Cu layers show various texture changes depending on the individual layer thickness (ranging between 100nm and 1nm). Generally, with decreasing individual layer thickness and increasing annealing temperature the f.c.c. content in the multilayers increases at the expense of the h.c.p. fraction.