We present large velocity gradient (LVG) and nonlocal radiative transfer calculations involving the rotational and hyperfine structure of the spectrum of N₂H⁺, with collisional rate coefficients recently derived by us. The goal of this study is to check the validity of the assumptions made to treat the hyperfine structure and to study the physical mechanisms leading to the observed hyperfine anomalies. We find that the usual hypothesis of identical excitation temperatures for all hyperfine components of the J=1-0 transition is not correct within the range of densities existing in cold dense cores, i.e., a few 10⁴