The loading-unloading compression behavior and the oligo cyclic behavior of pure epoxy and graphene-epoxy nanocomposites are investigated since the systematic evaluation of the mechanical behavior under cyclic loading is of great importance in the development of damage characterization and fatigue models for polymer composites. High purity graphene nanoflakes (GNF) are synthesized by electric arc discharge method, and the manufacturing of graphene epoxy nanocomposites is done using solution blending. The structural characterizations of produced GNF are performed using several techniques such as transmission electron microscopy (TEM), Raman spectroscopy and Brunauer-Emmett-Teller (BET). Oligo quasi-static strain-controlled cyclic tests are performed at the elastic (or viscoelastic) region, around yield and after softening at the viscoplastic region. Comparing the behavior under compression, loading-unloading and oligo (repeated) cycled reveals that prehistory does not have much effect on the subsequent behavior. The change in the elasticity modulus during repeated cyclic compression is determined. It is observed that elasticity modulus decreases initially, and then, it progressively increases with the increase in applied maximum strain. Compared to epoxy, the yield stresses of graphene-epoxy decrease in both strain rates and a small increase in the elasticity modulus of graphene-epoxy is observed at low strain rate (1.E-4 /s).