[en] A theory of radiative muon capture, with applications to nuclear spin and isospin doublets, is formulated on the basis of the conservation of the hadronic electromagnetic current, the conservation of the hadronic weak polar currents, the partial conservation of the hadronic weak axial-vector current, the SU(2) x SU(2) current algebra for the various hadronic current, and a simplifying dynamical approximation for the hadron-radiating part of the transition amplitude: the ''linearity hypothesis''. The resultant total transition amplitude, which also includes the muon-radiating part, is worked out explicitly and applied to treat the processes μ^-p → ν/sub μ/nγ and μ^-3He → ν/sub μ/ ³Hγ