The AC hopping conductivity is written in terms of the Green matrix of the linearized rate equations. The diagonal elements of the Green matrix are eliminated and the configuration average of the hopping conductivity is then expressed as the fourth moment of a 'diffusion function' of frequency and intersite distance. The behaviour of the diffusion function and the AC conductivity is discussed at high frequencies, intermediate frequencies and low frequencies for both degenerate and nondegenerate statistics. A variational formula is given for the real part of the configuration average of the AC conductivity. It provides a lower bound and has the additional merit that the configuration average may be taken at the outset of the variational calculation.