Spectrally resolved four-wave mixing measurements in wurtzite GaN show a de
pendence of the quantum beats' phase on incident polarizations. We observe
different phases at the A-exciton and the B-exciton resonances when excitin
g with circular polarized light. The observed phase difference indicates th
at exciton-exciton interaction plays a major role in the quantum beat proce
ss. The developed analysis allows us to conclude that the spins of the elec
trons rather than the holes give the major contribution to the exciton-exci
ton interaction in GaN.