Co/X multilayers (X = Ir, Au, Cu, Pd) were investigated by NMR. All multilayers contained mainly fcc Co. A significant number of stacking faults is present giving a positive contribution to the magnetic volume anisotropy. In Co/Cu a linear dependence of the strain on the inverse Co thickness was observed. This might give rise to an apparent interface anisotropy. Signals due to interface atoms in Co/Cu indicate an atomic roughness of theinterfaces of about one atomic distance.