The interdiffusion in the amorphous CoN/CN soft X-ray multilayers is investigated quantitatively by monitoring the enhancement of the first order modulation peak on annealing in the temperature range of 473-523 K. The effective interdiffusion coefficient measured is as low as 10(-25) m(2) s(-1). The comparison with the results of Co/C system [H.L. Bai at al., Thin Solid Films. 286 (1996) 176-183] indicates that the following three features are noticeable : (1) the interdiffusion critical wavelengths were calculated as 2.00-2.04 nm at temperatures ranging from 473 to 523 K, which an equal to those of Co/C multilayers within the experimental error. indicating that the interdiffusion behaviours in the CoN/CN multilayers art still decided by the thermodynamic properties of the Co-C system, (2) the effective interdiffusivities and macroscopic diffusion coefficients are lower, and (3) the activation energy for diffusion is higher, The results imply that it is possible to improve the thermal stability of Co/C multilayers by doping with N. The mechanisms resulting in the features are clarified in detail.