Time-resolved photoluminescence measurements of carrier lifetimes in modulation-doped (100 Å) AlxGa1-xN/(100 Å) GaN multiple quantum well heterostructures are reported. The photoluminescence (PL) spectrum exhibits several lines associated with recombination of carriers from multiple excited electron states to the hole ground state. The PL decay times associated with ground state recombination, e0h0, are found to be much longer than the inverse repetition rate of our system (20 μs) and estimated to be 9 ms. The experimental lifetimes associated with carrier recombination from excited states vary between 4 μs for the first excited state, e1h0, and 4.5 ns for the fourth excited state, e4h0. These lifetimes are in very good agreement with a self-consistent calculation of radiative recombination lifetimes which takes into account piezoelectric and spontaneous polarization. The significant differences in recombination lifetimes are the result of the large built-in electric field in the wells (0.5 MV/cm).