In a crystal lacking inversion symmetry, in the presence of spin-orbit
interaction, the spin degeneracy is in general removed at k not equal
0 even in the absence of an external magnetic field. Such is the case
for bulk III-V semiconductors having the zincblende structure. In nan
ostructures having a reduced symmetry with respect to the bulk, additi
onal zero-field spin-splitting mechanisms are allowed. The interplay b
etween the different spin-orbit interactions is thoroughly investigate
d and the relevance of the spin-splittings for excitonic properties is
addressed. In particular, the competition between intraexciton exchan
ge and single particle spin flips in the relaxation of the exciton lum
inescence polarization is analysed.