The influence of Si/B content and annealing conditions on the microstructure and magnetic properties of melt-spun FeSiB-CuNb alloys were investigated. Heating at temperatures between 750 and 800 K leads to the formation of a nanocrystalline Fe(Si) phase in the amorphous matrix. Nanostructure is stable in an extended annealing temperature/time range; by increasing the annealing temperature only an enhancement of the volume fraction of the nanophase and a slight increase of the mean grain size of the nanocrystals are found. Kinetic analysis of the nanocrystallization reaction gives an anomalously small value of the Avrami exponent and it should be related to some special features of the nucleation and growth mechanisms in FINEMET-type allows. Heating at temperatures between 900 and 950 K produces full transformation of the amorphous matrix. Transition temperatures mean grain size of the nanocrystals and their silicon content, estimated from the Curie temperature, show composition dependence.