The article explores the relaxation dynamics and viscoelastic properties in three types of metallic glasses with distinct β relaxation behavior. The study reveals that in systems with significant β relaxation, stress relaxation and creep experiments show a transition from two-step to one-step relaxation as the temperature rises. This phenomenon is absent in systems with weaker β relaxation. The two-step relaxation process is modeled using a double Kohlrausch-Williams-Watts equation, and the relaxation times align with the Arrhenius relationship. By combining fitted activation energies with theoretical analysis, the relaxation processes are attributed to β and α relaxations. The study provides a comprehensive understanding of the relationship between dynamic relaxation and viscoelasticity, offering new strategies for probing the complex relaxation behaviors of glasses from a viscoelastic perspective. The research highlights the significant impact of β relaxation on viscoelastic deformation, particularly in systems with distinct β peaks, where the single-step relaxation process at high temperatures transitions to a two-step relaxation process at low temperatures. This finding enhances the understanding of relaxation behavior in glassy systems and establishes a direct link between complex relaxation behavior and static viscoelastic deformation.The article explores the relaxation dynamics and viscoelastic properties in three types of metallic glasses with distinct β relaxation behavior. The study reveals that in systems with significant β relaxation, stress relaxation and creep experiments show a transition from two-step to one-step relaxation as the temperature rises. This phenomenon is absent in systems with weaker β relaxation. The two-step relaxation process is modeled using a double Kohlrausch-Williams-Watts equation, and the relaxation times align with the Arrhenius relationship. By combining fitted activation energies with theoretical analysis, the relaxation processes are attributed to β and α relaxations. The study provides a comprehensive understanding of the relationship between dynamic relaxation and viscoelasticity, offering new strategies for probing the complex relaxation behaviors of glasses from a viscoelastic perspective. The research highlights the significant impact of β relaxation on viscoelastic deformation, particularly in systems with distinct β peaks, where the single-step relaxation process at high temperatures transitions to a two-step relaxation process at low temperatures. This finding enhances the understanding of relaxation behavior in glassy systems and establishes a direct link between complex relaxation behavior and static viscoelastic deformation.