The fluctuation-dissipation theorem relating spontaneous equilibrium fluctuations to the conductance in a dissipative thermodynamic system is extended to the case of several variables, using a quantum statistical analysis. The conductance matrix is shown to be subject to certain symmetry relations, providing a generalization of the Onsager reciprocity theorem. The susceptance matrix is also shown to be subject to similar symmetries. The symmetries apply to all frequency components, and hence to arbitrary transient processes.