© 2021, The Author(s), under exclusive licence to Springer Nature B.V.In this work, graphene–epoxy nanocomposites are produced for two different graphene fractions (0.1 and 0.5 wt%). Three-roll milling is used as the main strategy to achieve a homogeneous dispersion and prevent agglomeration. To improve the interfacial bonding between graphene nanoflakes (GNF) and epoxy matrix, GNFs are functionalized using Triton X-100 as a surfactant. The effectiveness of this functionalization is investigated using Raman spectroscopy and Fourier transform infrared spectroscopy (FT-IR). These spectroscopy results show that the Triton X-100 molecules are successfully adsorbed on the surface of GNFs. To investigate the total viscoelastic–viscoplastic behavior of the nanocomposites, compression tests at three different quasistatic strain rates (1.E-1, 1.E-2, 1.E-3 /s), creep tests at two different stress levels and relaxation tests at two different strain levels are performed. The total time-dependent mechanical behavior of the produced nanocomposites is therefore characterized comprehensively. Elasticity-modulus values obtained from compression tests increased up to 29% and yield stress increased up to 18%. In creep tests, it is observed that the creep strain decreased 32% and 65% at 50 and 100 MPa stress levels, respectively, at 0.1 wt% functionalized graphene flakes (f-GNF)–epoxy nanocomposite. At the same time, with the addition of 0.1 wt% f-GNF to epoxy, during relaxation tests, the stress drop decreased up to 47% compared to pure epoxy at a 3.16% constant strain level. Both creep and relaxation resistance improved when compared to pure epoxy. This total improvement in the mechanical behaviors is explained with the effective dispersion of the GNFs and also a strong interface between the GNFs and the epoxy matrix.