We report a systematic study of the photoluminescence (PL) properties of a series of nearly lattice-matched (LM) GaN/(Al,In)N single quantum well (SQW) samples, with well thickness ranging from 1.5 to 5 nm, grown by metalorganic vapor phase epitaxy. Temperature dependent PL and time-resolved PL measurements reveal similar trends among the studied SQW samples, which also indicate strong localization effects. The observed PL energy behavior, akin to the S-shape, accompanied first by a narrowing and then a broadening of the PL line width with increasing temperature, closely resemble previous observations made on the more established (In,Ga)N/GaN QW system. The similar trends observed in the PL features of those two QW systems imply that the PL properties of LM GaN/(Al, In) N SQW samples are also governed by localized states. The effects of carrier transfer among these localization sites are clearly observed for the 3 nm thick QW, evidenced by an increasing PL intensity in the lower energy spectral window and a concomitant increase in the corresponding PL decay time. Time-resolved data corroborate the picture of strongly localized carriers and also indicate that above a well thickness dependent delocalization temperature carrier distribution across the localized sites reaches thermal equilibrium, as the PL decay times over different spectral regions converge to the same value. Based on the difference between the calculated QW ground state transition energy, obtained using the envelope wave function formalism, and the measured PL energy, a localization energy of at least a few hundreds of meV has been extracted for all of the studied SQW samples. This rather large value also implies that In-related localization effects are more pronounced in the GaN/(Al, In) N system with respect to those in the (In, Ga) N/GaN one for a similar In content. Published by AIP Publishing.