The ratio between the two stable isotopes of nitrogen, 14N and 15N, is well measured in the terrestrial atmosphere (~272), and for the pre-solar nebula (~441, deduced from the solar wind). Interestingly, some pristine solar system materials show enrichments in 15N with respect to the pre-solar nebula value. However, it is not yet clear if and how these enrichments are linked to the past chemical history because we have only a limited number of measurements in dense star-forming regions. In this respect, dense cores, which are believed to be the precursors of clusters and also contain intermediate- and high-mass stars, are important targets because the solar system was probably born within a rich stellar cluster, and such clusters are formed in high-mass star-forming regions. The number of observations in such high-mass dense cores has remained limited so far. In this work, we show the results of IRAM-30 m observations of the J = 1−0 rotational transition of the molecules HCN and HNC and their 15N-bearing counterparts towards 27 intermediate- and high-mass dense cores that are divided almost equally into three evolutionary categories: high-mass starless cores, high-mass protostellar objects, and ultra-compact Hii regions. We have also observed the DNC(2–1) rotational transition in order to search for a relation between the isotopic ratios D/H and 14N/15N. We derive average 14N/15N ratios of 359 ± 16 in HCN and of 438 ± 21 in HNC, with a dispersion of about 150–200. We find no trend of the 14N/15N ratio with evolutionary stage. This result agrees with what has been found for N2H+ and its isotopologues in the same sources, although the 14N/15N ratios from N2H+ show a higher dispersion than in HCN/HNC, and on average, their uncertainties are larger as well. Moreover, we have found no correlation between D/H and 14N/15N in HNC. These findings indicate that (1) the chemical evolution does not seem to play a role in the fractionation of nitrogen, and that (2) the fractionation of hydrogen and nitrogen in these objects is not related.