We report on the time evolution of the magnetization measured under constant applied field in highly homogeneous amorphous CoZrDy thin films. Our results show that the thermally activated reversal proceeds after a time interval (waiting time) whose magnitude depends on the field value and during which the macroscopic state of the sample evolves very slowly. Also, and differently from the relaxation of systems having distributed properties, the observed reversal is accomplished in a finite time interval. The experimental data are adequately reproduced by the relaxation of a 2D micromagnetic model which clearly suggests that the thermally activated reversal takes place through a nucleation-propagation sequence also showing some indications of collective behavior.