  We study the radiative decays B -> V gamma (where V=rho, K^*) in the
framework of QCD factorisation, and in particular the hard-spectator
contributions to the decay amplitudes. For the phenomenologically significant
chromomagnetic operator, we show by an explicit next-to-leading-order
computation that the spectator interactions factorise in the heavy-quark limit,
i.e. that they can be written as the convolution of a hard-scattering kernel,
computable in perturbation theory, and of the light-cone distribution
amplitudes for the B and V mesons which contain the soft physics. The presence
of an intermediate scale of order sqrt{Lambda_QCD M_B} leads to the presence of
Sudakov logarithms. We indicate how the proof of factorisation can be extended
to other (four-quark) operators.
