Abstract: The energy dependence of the cross section of the (n,p) and (n,d) reactions on C-nat has been studied for the first time at the nTOF facility at CERN, from the particle detection threshold up to 25 MeV. The measurement was performed with two telescopes made of position-sensitive silicon Delta E-E detectors, covering the angular range from 20 degrees to 140 degrees. A detector efficiency has been determined by means of Monte Carlo simulations of the experimental setup. Various assumptions on the angular distributions and branching ratios of the excited levels of the residual B-11, B-12, B-13 nuclei were considered. In particular, theoretical calculations based on the TALYS-2.0 code were used and the systematic uncertainties in the analysis results were determined from the variations in these distributions. The nTOF data on the (n,p) and (n,d) reaction on carbon are characterized by a higher accuracy and wider energy range than currently available in literature. A comparison with current evaluations from different libraries reveals a rather significant disagreement with the n_TOF results, while a remarkable agreement is observed with the prediction of TALYS-2.0 for this light element.