Context. The increased sensitivity and high spectral resolution of millimeter telescopes allow the detection of an increasing number of isotopically substituted molecules in the interstellar medium. The 14N/15N ratio is difficult to measure directly for molecules containing carbon. Aims. Using a time-dependent gas-phase chemical model, we check the underlying hypothesis that the 13C/12C ratio of nitriles and isonitriles is equal to the elemental value. Methods. We built a chemical network that contains D, 13C, and 15N molecular species after a careful check of the possible fractionation reactions at work in the gas phase. Results. Model results obtained for two different physical conditions that correspond to a moderately dense cloud in an early evolutionary stage and a dense, depleted prestellar core tend to show that ammonia and its singly deuterated form are somewhat enriched in 15N, which agrees with observations. The 14N/15N ratio in N2H+ is found to be close to the elemental value, in contrast to previous models that obtain a significant enrichment, because we found that the fractionation reaction between 15N and N2H+ has a barrier in the entrance channel. The high values of the N2H+/15NNH+ and N2H+/N15NH+ ratios derived in L1544 cannot be reproduced in our model. Finally, we find that nitriles and isonitriles are in fact significantly depleted in 13C, thereby challenging previous interpretations of observed C15N, HC15N, and H15NC abundances from 13C containing isotopologues.