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Two reciprocity theorems are derived which are valid for fields whose sources may have arbitrary time dependence. The first theorem involves the electromagnetic potentials, and the second is in terms of the electric and magnetic fields directly. In both cases, it is necessary to make use of the advanced as well as the retarded solutions to Maxwell's equations. Some properties of the theorems are discussed, and, as an application, the second theorem is used to derive a variational expression for scattering of electromagnetic waves from a perfect conductor.