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This article presents a computational homogenization framework for viscoelastic composites within the framework of non-ordinary state-based peridynamic theory. The motivation to develop this framework stems from the desire to develop a homogenization scheme that can model processes and phenomena that are driven by nonlocal behaviour such as size effect and fracture for which frameworks based on the classical continuum theory lack the capability of modelling. The proposed framework was used to calculate the effective properties in both time and frequency domains of two viscoelastic matrix-inclusion composite systems, one with an elastic inclusion and viscoelastic matrix, and the other with viscoelastic inclusion and matrix. The results of calculations were found to compare well with results from the literature. A parametric study was also conducted to investigate the influence of nonlocal interaction on the effective properties by varying the horizon size. Results showed that increasing the degree of nonlocality reduces the stiffness of the composite system as well as increase its rate of creep. The capability to account for nonlocal interaction highlights the potential of this proposed scheme to provide a more comprehensive understanding of the behaviour of viscoelastic composite materials over a wide range of material behaviour. [ABSTRACT FROM AUTHOR]