In this work, two series of biodegradable nanocomposites of poly(ethylene succinate) (PESu) containing either graphene oxide (GO) or organomodified GO (org-GO) with 1-dodecylamine have been prepared and studied. GO was synthesized using a modified Staudenmaier method from of powdered graphite and PESu/GO and PESu/org-GO nanocomposites with GO or org-GO concentrations 0.5, 1 or 2.5 wt% were prepared with the solvent evaporation method. The nanocomposites were characterized with several techniques. Microscopic and XRD study showed intercalated dispersion of GO into PESu matrix while in the case of org-GO fully exfoliated nanocomposites were obtained. Isothermal and nonisothermal crystallization was studied from the melt or from the glass state by using DSC and it was found that nanocomposites crystallized faster than the neat PESu under both conditions. Crystallization rates increased with increasing filler content and it seems that GO have higher crystallisation effect than org-GO. This is due to the stronger interactions that are taking place between PESu and GO, as was confirmed by FTIR and DSC. In the case of the nanocomposites interesting crystalline morphologies and different to those for neat PESu, were observed with PLM. Enzymatic hydrolysis studies revealed that nanocomposites have higher hydrolysis rates than neat PESu, while GO accelerates in higher extent the hydrolysis of PESu than org-GO.