Differential scanning calorimetry (DSC) measurements with different temperature programs were used to study the crystallization kinetics of Ni81P19 amorphous ribbons quenched from melt at different temperatures (920-1600 degrees C) and from a constant melt temperature (920 degrees C) at different quenching rates leading to different thickness. A mathematical model was proposed assuming that the nuclei are formed during the preparation and pretreatment of the samples and grow during the DSC experiments. Its validity was proved by the non-linear least squares evaluation of 44 DSC experiments, This model describes our experiments better than Avrami-Erofeev equation.