We present inelastic neutron scattering (INS) experiments on various types of cellulose revealing the universal nature of the disordered regions from the point of view of low-energy dynamics. Using INS in combination with the deuteration of polar groups technique, we have studied the dynamic response of hydroxyl groups, chi " within cellulose: chi(ac)"(omega) from regions accessible to water was found to be distinctly different from chi(ac)"(omega) obtained from the inaccessible crystal cores. The shape of chi(ac)"(omega) does not depend on the sample origin and, therefore, is independent of its crystallinity. Our study includes the comparison of different native cellulose specimens with (i) a completely disordered reference sample and (ii) a sample where the intracrystalline hydroxyl groups have been deuterated. Thus, we can state that the accessible regions are identical to disordered regions. These regions, which include the crystal surfaces, possess a common dynamic signature.