In view of possible existence of the nucleonic sccond·class current, the weak charged urbaryonic and leptonic V-A currents are generalized so as to contain derivative currents by assuming two-component neutrino theory and baryon-lepton correspondence. Values of parameters associated with the derivative currents of lepton are determined from p-, 'i:- ·and K-decays. The generalized currents can explain ~ parameter of the p-decay. §I. Introduction Recently some experiments have been performed to study the possible existence of second-class currents. Measurements 11 of decay asymmetries in polarized nuclei showed that the coupling constants associated with the second-class 1 seem to be larger than the corresponding theoretical values expected from the SU (2) symmetry breaking. On the other hand, the latest experimental results in aligned nuclei are consistent with absence of the second-class current. 1 Although the experimental situation about the second-class current is in an unsettled state, it will be interesting to examine some consequences front the assumption of the existence of the second-class currents both in urbaryonic and leptonic levels. We generalize the weak charged V-A currents so as to involve derivative terms such as tensor (6' a,l (f§ +a) S), pseudo-tensor (u aS75 (fJ + 8) S), scalar (i (fJ +a) a) and pseudo-scalar (ir5 cf§ +a) a) as well as vector Cr a) and axial-vector Cr ar5) terms. We assume the following which gives further limitations on the form of the currents: i) The current is hermitian as well as T-in variant. ii) Neutrinos (v~, Ve) are massless with two components and the neutrinos and anti-neutrinos are left handed and right-handed, respectively. iii) Baryon-lepton (B-L) correspondence 41~61 is adopted. These assumptions imply that a P-type urbaryon appears as left-handed in the urbaryon current and that the coupling constant of the tensor term becomes equal to that of the pseudo-tensor one. \Ve show that the leptonic current involving derivative terms well reproduces the experimental value of e) parameter in the ,11-decay, while the com-entional V-A current theory with two-component neutrinos 81 shows some departure from experimental results. This conventional V-A current well reproduces experimental results except for the c; parameter. The theoretical value is c;v-A = 1, whereas the experimental value is slightly smaller; c;exp = 0.972 ± 0.013. 71 In a weak-intermedi