Picosecond time-resolved photoluminescence is used to investigate the recombination dynamics of excitons in samples which ail contain four GaN-AlxGa1-xN quantum wells of respective widths of 4, 8, 12 and 16 molecular monolayers, grown by molecular beam epitaxy. The compositions and thicknesses of the barriers have been varied, in order to change the electric fields induced by piezo- and pyro-electric effects. The dependences of experimental decay times with barrier characteristics indicate the presence of efficient inter-well carrier escaping. Calculations of electronic tunneling times versus barrier width show that the present carrier escaping is enhanced by some additional process, such as scattering by impurities or composition fluctuations in the barriers.