The structural stability of CoN/CN soft X-ray multilayers has been investigated by using complementary measurement techniques. Annealing in the low-temperature range of 473-523 K, we find three interdiffusion features, different from Co/C multilayers [H.L. Bai et al.: Thin Solid Films 286, 176 (1996)]. (1) The interdiffusion critical wavelengths were calculated as 2.00-2.04nm at temperatures ranging from 473 to 523 K, which is equal to those of Co/C multilayers within the experimental error, indicating that the interdiffusion behaviours in the CoN/CN multilayers are still decided by the thermodynamic properties of the Co-C system. (2) The effective interdiffusivities and macroscopic diffusion coefficients are smaller. (3) The activation energy for diffusion is larger. The features imply that it is possible to improve the thermal stability of Co/C multilayers by doping with N atoms.