  The shape coexistence in the nuclei $^{182-192}$Pb is analyzed within the
Hartree-Fock-Bogoliubov approach with the effective Gogny force. A good
agreement with the experimental energies is found for the coexisting spherical,
oblate and prolate states. Contrary to the established interpretation, it is
found that the low-lying prolate and oblate $0^+$ states observed in this mass
region are predominantly characterized by neutron correlations whereas the
protons behave as spectators rather than playing an active role.
