Among amorphous films of rare earth-transition metal (RE-TM) alloys as exchange-biasing layers in magnetoresistive heads and spin-valve sensors, the amorphous Tb-Co films have most high practical potential. In the present work the influence of the temperature and the heat treatment parameters on the structure and magnetic properties was studied for exchange bias FeNi/Tb35Co65 bilayers annealed in vacuum or a nitrogen flow. A simple explanation of the dependence of the magnetic properties on the temperature and the heat treatment parameters connected with structural changes in each one of the layers was proposed.