MBE-grown samples containing several GaN-AlxGa1-xN quantum wells of varying widths are studied by picosecond time-resolved photoluminescence. Extremely strong built-in electric fields are present in such systems, due to piezoelectric and pyroelectric effects. Our results first show that we change the field In the quantum wells by changing the thickness of the separation barriers, as predicted by theory. We calculate the dependence of exciton radiative lifetimes on barrier thickness and compare these predictions with experimental data. We find that the carrier lifetimes are controlled by efficient nonradiative inter-well transfers, rather than by radiative recombination alone. However, the observed barrier-thickness dependence of decay times is inconsistent with a mere tunnel effect. Extrinsic processes, such as scattering by impurities ol composition fluctuations in the barriers are tentatively invoked to explain our results.