Abstract: The correlation between stress relaxation behavior and the evolution of microstructural heterogeneity of Zr-based amorphous alloys was probed. Amorphous alloy is the typical non-equilibrium solid system. Stress relaxation process is accompanied by aging effect of the amorphous alloy. In the current work, the coupling evolution of the most probably characteristic time \tau and stretched exponent \;\beta in the classical stretched function is considered for the first time, indicating the time dependence of structural state in the stress relaxation process. Based on the evolution of the non-equilibrium structure state of the amorphous alloys, the aging effect in the stress relaxation behavior was clarified. The results demonstrated that the stress relaxation behavior of amorphous alloys has non exponential characteristics. The exponential relaxation form of single characteristic time and the finite spectrum method of finite characteristic time cannot describe accurately the experimental results. This phenomenon is ascribed to the continuous distribution of the characteristic time spectrum caused by the microstructural heterogeneity of amorphous alloys. In addition, the stress relaxation behavior in the apparent elastic region is independent of the initial strain, which is due to the macroscopic flow nature of the stress relaxation behavior. Elastic and anelastic reversible deformation is transformed into viscoplastic (irreversible) deformation. Finally, Evolution of structural parameters caused by aging during stress relaxation is considered, which is reflected in the increase of characteristic time \tau and the decrease of stretched exponent \;\beta .