Characterization and analysis of photoresponse in p-n diodes with embedded (In,Ga)N-GaN multiple-quantum-well (MQW) structures are reported. Their dependence on the number of wells and In composition are considered. The influence of device structure on electric fields in the active region and on device responsivity has also been studied. Theoretical considerations as well as photocapacitance and photocurrent measurements show that the position of quantum wells (QWs), either in the quasi-neutral region or in the space charge region, is a critical factor in the collection efficiency. Hence, device photoresponse is not proportional to the number of QWs in photovoltaic mode. Present p-MQW-n devices show a promising performance as UVA and visible photodetectors, with detectivities, D*, higher than 1.2×1012 cm·Hz12/·W-1 and rejection ratios higher than 103.