The P-odd isoscalar interaction in the NN system generated by two-pion
exchange between nucleons is studied. The mechanism for this interact
ion includes the emission and subsequent absorption of a pi meson by a
nucleon, with the pion undergoing scattering on the second nucleon vi
a P-odd exchange between these two processes. In the spirit of the vec
tor-dominance model, the weak pi-N --> pi-N scattering occurs as a res
ult of rho-meson exchange between the nucleon and the pi meson. At low
energies of the NN system and, consequently, small momentum transfers
, the weak pi-N scattering occurs practically as a contact interaction
. Meanwhile, the range of the resulting weak NN interaction is determi
ned by the peripheral nature of pi-meson emission by the nucleon and i
s greater-than-or-equal-to 0.4 F. The main uncertainty in the calculat
ion of the contribution of the two-pion exchange mechanism to the P-od
d correlation is related to the poor knowledge of the constant describ
ing the isoscalar P-odd interaction of the rho-meson with the axial nu
cleon current. For realistic values of the latter the contribution of
isoscalar two-pion exchange to the longitudinal analyzing power in low
-energy pp scattering is congruent-to 10-15%.