We show that the first moment of the spin-dependent structure function
g(1)(gamma)(x, Q(2)) of a real photon vanishes independent of the mom
entum transfer Q(2) it is probed with. This result is non-perturbative
: it holds to all orders in perturbation theory in abelian and non-abe
lian gauge theory and at every twist. (C) 1998 Elsevier Science B.V. A
ll rights reserved.