In this study, the aligned (A) and randomly oriented (R) polycaprolactone (PCL-A and PCL-R) and PCL/collagen (PCL/Col-A and PCL/Col-R) nanofibers were electrospun onto smooth PCL membranes (PCLMs) prepared by solvent casting. In order to investigate the effects of chemical composition and nanotopography of fibrous surfaces on proliferation and on neural differentiation of mesenchymal stem cells (MSCs), adipose and bone marrow-derived rat MSCs (AdMSCs and BMSCs) were cultivated in suitable media i.e. inducing medium containing basic fibroblast growth factor (bFGF) and epidermal growth factor (EGF), and cell maintenance medium (CMM). BMSCs adhered and proliferated on all nanofibrous membranes more efficiently than AdMSCs. PCL/Col-A was found as the most convenient surface supporting proliferation in both cell types. Immunofluorescence staining indicated that BMSCs and AdMSCs are prone for differentiation to oligodendrocytes more than they differentiate to other neuronal cell types. PCL-A nanofibrous membranes supported differentiation of MSCs to O4(+) (an oligodendrocytes surface antigen) cells in both culture media. The intensity of immunoreactivity of O4(+) cells differentiated from BMSCs on PCL-A was highest when compared with the other groups (p < 0.001). Some BIII-T signed neural cells were investigated on PCL-A nanofibrous membranes, but the intensity of immunoreactivity was lower than that of O4(+) cells. In conclusion, this study can be evaluated to establish the cell therapy strategies in neurodegenerative disorders, which are relevant to oligodendrocyte abstinence using BMSCs or AdMSCs on aligned nanofibrous membranes.