The nanocrystallization process taking place during isothermal annealing at 490 degrees C in Fe_73.5CuNb₃Si_17.5B₅ amorphous alloy was studied as a function of annealing time by using transmission Mossbauer spectroscopy. Two different stages were found: a first one where mainly changes in the short-range order parameters of the amorphous phase occur, and a second one where nanocrystals with DO₃ structure appear. The silicon content in the nanocrystals decreases with annealing time to a final value of about 22 at.%. The first stage is also observed after 1 hour annealing at 450 degrees C or after cycling the amorphous sample from room temperature to 490 degrees C at a rate of 160 degrees C min^-1 several times. The magnetic moments in the amorphous phase tend to align parallel to the surface of the ribbon especially in the first stage of nanocrystallization. The nanocrystalline phase formed in the second stage shows also a preferential magnetic orientation parallel to that surface. The existence of two stages is corroborated by differential scanning calorimetry, transmission electron microscopy and image analysis. The overall observations strongly suggest that nanocrystallization is driven by nucleation and growth.