Exciton resonances are observed in the dielectric functions of wurtzite AlN by spectroscopic ellipsometry for the electric field vector parallel and perpendicular to the optical axis. The temperature dependence of these excitons is analyzed in detail. From the dielectric functions, reflectivity spectra are calculated and compared to experimentally obtained reflectivity, perfect agreement is found. The relative oscillator strengths of excitons showing different symmetries are discussed yielding an unambiguous assignment of free excitons formed by holes from the highest valence band. As a consequence, a negative exciton spin-exchange coupling constant of j = -4 meV is derived.