Magnetic properties of amorphous and nanocrystalline Fe31Ni50Zr7B12 and Fe41Ni40-xCoxZr7B12 (x=10,20) alloys are studied by an unconventional “rf-Mössbauer” technique. The introduction of Co atoms into FeNiZrB amorphous and nanocrystalline alloys leads to a large increase of anisotropy field that limits the rf-collapse effect. The rf-Mössbauer measurements are very useful for the estimation of magnetic anisotropy field. The rf sidebands vanish when the nanocrystalline structure is formed. The rf-induced crystallization effect observed in Co-containing alloys is particularly strong in magnetostrictive amorphous alloys and in nanocrystalline alloys containing significant fraction of amorphous matrix. This effect does not occur in Co-free alloy.