Period expansion of Co/C and CoN/CN soft x-ray multilayers has been investigated by x-ray diffraction and Raman spectroscopy. Below the anneal temperature of 400℃, the period expansion (<12%) of Co/C multilayers is mainly caused by the graphitization of the amorphous carbon layers. By 500 oC, the crystallization and agglomeration of Co layers induce an enormous period expansion (～40%). The period expansion of CoN/CN multilayers is only 4% at 400℃, which is much smaller than that of Co/C multilayers. The interface patterns of the CoN/CN multilayers still exist even if they were annealed at 700℃ The Raman spectroscopy analyses indicate that the formation of the sp3 bonding can be suppressed effectively by doping N atoms, and thus the period expansion is decreased considerably at annealing temperatures below 600℃. The significant suppression of grain growth above 600℃ is believed to be attributed to the coexistence of hcp and fcc Co structures induced by interstitial N atoms, which cause the high-temperature period expansion decrease. The results also imply that the structural stability of Co/C soft x-ray multilayers can be significantly improved through doping N atoms.