Polarized properties of both the singlet and triplet ground exciton st
ates in the photoluminescence and transmission spectra of crystalline
GaTe are explained based on the possible symmetry properties of the en
ergy band edge of GaTe. Some experimental results about excited excito
n states in GaTe are presented and discussed. The energy positions of
exciton series in GaTe follow the three-dimensional direct allowed Wan
nier exciton formula just as in the other III-VI layered compounds of
GaSe and InSe. The nonthermalized, ''hot'' nature of excitons inside G
aTe under higher optical excitation intensities is also discussed.