  We present a complete calculation of the Leading Order QCD corrections to the
quark level decay amplitude for b -> s gamma gamma and study their relevance
for both the inclusive branching ratio BR(B -> X_s gamma gamma) and for the
exclusive decay channel B_s -> gamma gamma. In addition to the uncertainties in
the short distance calculation, due to the choice of the renormalization scale,
an appreciable uncertainty in both B_s -> gamma gamma and B -> X_s gamma gamma
is introduced by the matrix element calculation. We also briefly discuss some
long distance effects, especially those due to the eta_c resonance for the
inclusive rate. Finally, the analysis of the IR singularities of the two photon
spectrum in the inclusive case is given.
