The degree of structural relaxation, the nucleation process and the early stage of nanocrystallization are studied in FINEMET type precursor alloy using permeability and power loss measurements. It is pointed out, that -besides the development of nanograin structure,- the antecedent structural relaxation and nanograin nucleation do also contribute significantly to the development of the magnetic softness and the power loss decrease in these alloys, however, they are often attributed solely to the "exchange softening" characteristic to the nanocrystalline structure. The comparison of the domain structure in as-quenched, nucleated and fully nanocrystalline state does also support the conclusions drawn from the permeability and loss measurements.