The model of hopping excitons in semiconductors proposed by Baranovskii et al (1998 Phys. Rev. B 58 13081) has been modified and applied to explain sharp lines observed in micro-photoluminescence (μ-PL) spectra of GaInNAs alloys and their changes with excitation power and temperature. Instead of two types of recombination centres (radiative and nonradiative centres) introduced by Baranovskii et alwe have proposed one kind of localization centre with radiative and nonradiative rates. Such a modification is justifiable due to our recent experimental observations for GaInNAs alloys and allows us to explain the fast thermal quenching of localized emission from this alloy. Our simulations clearly show that the individual sharp PL lines observed at low temperatures appear for this material due to exciton hopping between localization centres. Taking into account saturation effects and the exciton dissociation phenomenon, it has been shown that the observed changes in power- and temperature dependent μ-PL spectra can be excellently reproduced by the modified model.