The static and dynamic magnetic properties of the nanocrystalline soft magnetic FeNbB alloys consisting of Fe-nanograins embedded in an amorphous matrix were investigated by means of dc and ac susceptibility, magnetization and hysteresis loop measurements in a wide temperature range. We show that these alloys exhibit particular complex magnetic behaviour versus temperature. The spin-glass like behaviour at cryogenic temperatures is followed by a very soft magnetic behaviour at intermediate temperatures, and finally, a marked magnetic hardening due to decoupling between the nanograins is observed when temperature approaches the Curie temperature of the amorphous matrix. Upon further increase of temperature, the thermal relaxation of magnetization plays a dominant role. The results are discussed within a model that takes into account the presence of weakly magnetic Nb-rich shells around the nanocrystalline grains.Introduction The reduction of the grain sizes to the nanometer range may vary drastically the physical properties of materials, including the magnetic behaviour. Typical examples of such systems are nanocrystalline soft magnetic alloys prepared by a devitrification of the melt-spun amorphous precursors. The structure of these materials consists of the nanocrystalline grains dispersed in the surrounding amorphous matrix. An early report on the materials that exhibited significant reduction of coercivity after the grain sizes decreased to 10-20 nm was given by O'Handley et al.[1] for a devitrified Co-based meltspun alloy. The discovery of the excellent soft magnetic properties in the nanocrystalline alloys based on FeCuNbSiB, also called FINEMET