  The relativistic generalization of the Newtonian Lagrangian perturbation
theory is investigated. In previous works, the first-order trace solutions that
are generated by the spatially projected gravitoelectric part of the Weyl
tensor were given together with extensions and applications for accessing the
nonperturbative regime. We furnish here construction rules to obtain from
Newtonian solutions the gravitoelectric class of relativistic solutions, for
which we give the complete perturbation and solution schemes at any order of
the perturbations. By construction, these schemes generalize the complete
hierarchy of solutions of the Newtonian Lagrangian perturbation theory.
