It is studied the crystallization kinetics of the two amorphous Fe80Si6B14 and Fe82Si2B16 alloys doped with Ni and Mo additives (0.5-3.8% at.) as well as their magnetic properties. Doping increases the thermal stability of the base alloys that is manifested by a rise of the temperatures of formation of the primary alpha-Fe(Si) phase during the heating, by a smaller transformed volume fraction, and by the regular increase of values of effective crystallization activation energy for doped alloys. Their magnetic properties after optimal precrystallization heat treatments are on the level or exceed properties of conventional soft magnetic crystalline alloys including Fe-Ni-permalloys.