The distribution of the N/O element abundance ratios calculated by the detailed modelling of different galaxy spectra at z<4 is investigated. Supernova (SN) and long gamma-ray-burst (LGRB) host galaxies cover different redshift domains. N/O ratios in SN hosts increase due to secondary N production towards low z (0.01) accompanying the growing trend of active galaxies [active galactic nucleus (AGN), low-ionization nuclear emission-line region (LINER)]. N/O ratios in LGRB hosts decrease rapidly between z>1 and z~0.1 following the N/H trend and reach the characteristic N/O ratios calculated for the H II regions in local and nearby galaxies. The few short-period gamma-ray-burst (SGRB) hosts included in the galaxy sample show N/H<=0.04 solar and O/H solar. They seem to continue the low bound N/H trend of SN hosts at z<0.3. The distribution of N/O as a function of metallicity for SN and LGRB hosts is compared with star chemical evolution models. The results show that several LGRB hosts can be explained by star multibursting models when 12+log(O/H)<8.5, while some objects follow the trend of continuous star formation models. N/O in SN hosts at log(O/H)+12<8.5 are not well explained by stellar chemical evolution models calculated for starburst galaxies. At 12+log(O/H)>8.5 many different objects are nested close to O/H solar with N/O ranging between the maximum corresponding to starburst galaxies and AGN and the minimum corresponding to HII regions and SGRB.