Multiwalled carbon nanotubes (MWCNT) were surface modified firstly oxidizing them with a H2SO4/HNO3 mixture to obtain more reactive carboxylic groups on their surface and then higher functionality. Secondly the oxidized nanotubes (MWCNT-COOH) were dispersed in tetrahydrofuran (THF) and made react via esterification with a poly(hexamethylene carbonate-co-caprolactone)diol, a potentially biodegradable polyol with hydroxyl groups at its ends. Modification process steps were characterized using Fourier transform infrared spectroscopy, FT-IR, ultraviolet spectroscopy, UV, solubility in different solvents, thermo-gravimetric analysis, TGA, as well as atomic force microscopy, AFM. Results suggest that surface carboxylic groups are reactive enough to graft polymer chains onto their surface.