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[en] Novel amorphous Fe80(ZrxSi20-x-y)Cuy boron-free alloys, in which boron was completely replaced by silicon as a glass forming element, have been prepared in the form of ribbons by a melt quenching technique. The X-ray diffraction and Moessbauer spectroscopy measurements revealed that the as-quenched ribbons with the composition of x = 6-10 at. % and y = 0, 1 at. % are predominantly amorphous. DSC measurements allowed the estimation of the crystallization temperatures of the amorphous alloys. The soft magnetic properties have been studied by the specialized rf-Moessbauer technique in which the spectra were recorded during an exposure of the samples to the rf field of 0 to 20 Oe at 61.8 MHz. Since the rf-collapse effect observed is very sensitive to the local anisotropy fields it was possible to evaluate the soft magnetic properties of amorphous alloys studied. The rf-Moessbauer studies were accompanied by the conventional measurements of the quasi-static hysteresis loops from which the magnetization and coercive fields were estimated. It was found that amorphous Fe-Zr-Si(Cu) alloys are magnetically very soft, comparable with those of the conventional amorphous B-containing Fe-based alloys.