Annealed amorphous alloys have been investigated by means of AC magnetic susceptibility measurement and x-ray diffraction analysis. The amorphous (x = 15, 16, 20, 25 and 30) alloys annealed at 523 K for 180 min exhibit re-entrant spin-glass behaviour, while a direct transition from a paramagnetic to a spin-glass phase occurs in the amorphous alloys with x = 7.5, 10 and 33.3. For the amorphous alloy, the Curie temperature and the magnetic moment increase, but the spin freezing temperature decreases on annealing. The magnetic phase diagram for the amorphous Y - Fe alloy system in the annealed state is similar to that for many other amorphous Fe-based alloy systems in the as-prepared state. Increases in the atomic distance of Fe - Fe pairs and in the coordination number of the nearest-neighbour Fe atoms on annealing have been observed. These structural changes explain the changes in the magnetic properties for annealed amorphous alloys.