Forward-to-reverse bias step-recovery measurements were performed on In.07Ga.93N/GaN and Al.36Ga.64N/Al.46Ga.54N quantum-well (QW) light-emitting diodes grown on sapphire. With the QW sampling the minority-carrier hole density at a single position, distinctive two-phase optical decay curves were observed. Using diffusion equation solutions to self-consistently model both the electrical and optical responses, hole transport parameters τp = 758 ± 44 ns, Lp = 588 ± 45 nm, and μp = 0.18 ± 0.02 cm2/Vs were obtained for GaN. The mobility was thermally activated with an activation energy of 52 meV, suggesting trap-modulated transport. Optical measurements of sub-bandgap peaks exhibited slow responses approaching the bulk lifetime. For Al.46Ga.54N, a longer lifetime of τp = 3.0 μs was observed, and the diffusion length was shorter, Lp ≈ 280 nm. Mobility was an order of magnitude smaller than in GaN, μp ≈ 10−2 cm2/Vs, and was insensitive to temperature, suggesting hole transport through a network of defects.