We derive the expressions of the rearrangement terms of the residual interaction to be used in the framework of the second random-phase approximation with density-dependent forces. These expressions are deduced within a variational derivation of the second random-phase-approximation equations. It is found that the rearrangement terms appearing in the beyond-random-phase-approximation matrix elements (which couple one-particle–one-hole with two-particle–two-hole and two-particle–two-hole with two-particle–two-hole configurations) are different from the standard random-phase-approximation rearrangement terms. This result indicates that both the currently used prescriptions, namely (a) using the same type of rearrangement terms in random-phase-approximation and in beyond-random-phase-approximation matrix elements, and (b) neglecting the rearrangement terms in beyond-random-phase-approximation matrix elements, are not correct. The quality of the approximations (a) and (b) is checked by comparing the approximated and correct results in the case of the monopole and quadrupole isoscalar strength distributions for the nucleus 16O. It is found that both approximations lead to quite different strength profiles with respect to the result obtained by applying the full second random-phase-approximation method.