We consider, in the field-theoretical approach, a class of gravitational theories deducible by a variational principle in the “unrenormalized” pseudo-Euclidean space-time. At first order in the coupling constant f we require the theories to coincide with the Einstein one. Moreover we assume the Hilbert gauge which assure the exclusion of the vector component of the gravitational potential ψαβ. To get the higher order consistency we substitute the most general energy-momentum tensor\(\bar T_{\alpha \beta }^{(tot)}\) for the particle tensorT αβ (p) in the field equations. Requiring the latter to be deducible by a variational principle varying the potentials ψαβ, we get a Lagrangian which, varying the particle coordinates, gives the equations of motion. So we get a class of theories depending on 5 arbitrary parameters. To have observable quantities we have to “renormalize”. So we realize that, to satisfy the equivalence principle, we have to put one of the arbitrary parameters equal to zero. With this choice the class of theories coincides at second order with general relativity.