The total weak ΔS=0 hadronic current is usually split into CP-odd and CP-even, or first- and second-class currents. It is postulated that these currents obey an (SU(2) ⊗ SU(2)) ⊗ (SU(2) ⊗ SU(2)) algebra. This implies a set of Adler-Weisberger relations which, in particular, indicate the coupling of weak leptonic η→πlν decay as being of order one. It is possible to consider the strong interactions approximately invariant under the group generated by all these currents by introducing an additional set of scalar Goldstone bosons as well as C-odd pseudoscalar mesons. Since the latter seem not to exist, one has an alternative realization by CP doublets. As a special example, a generalized σ model is discussed. Further consequences are partial conservation of the second-class vector current and Goldberger-Treiman-type equations. Finally, the extension of the full algebra to leptons is discussed, which suggests the interesting fact that electrons and muons are CP partners of each other and the separate conservation of electron and muon numbers is a consequence of CP conservation.