We report on the experimental achievement of narrow ultraviolet excitonic and biexcitonic emission from GaN/AlGaN quantum wells. The very large biexciton binding energy (up to 12 meV) inhibits thermalization between the two species allowing to study the recombination kinetics of the biexciton gas. By performing resonant and nonresonant time resolved measurements, we elucidate the interplay between biexciton formation and exciton acoustic-phonon mediated relaxation within localized states.