In \ensuremath{\beta}'-${\mathrm{Gd}}_{2\mathrm{\ensuremath{-}}\mathit{X}}$${\mathrm{Eu}}_{\mathit{X}}$(${\mathrm{MoO}}_{4}$${)}_{3}$ the ${\mathrm{Eu}}^{3+}$ ion occupies two different crystallographic sites, leading to small differences in the respective energy-level schemes. At very low temperatures a one-phonon-assisted energy transfer and at higher temperatures a two-site nonresonant two-phonon-assisted energy transfer occurs from a ${\mathrm{Eu}}^{3+}$ ion on one site to a neighboring ${\mathrm{Eu}}^{3+}$ ion on the other site over a distance of 6.3 A\r{}. For x=2, there no longer is a distinction possible between the two sites because of inhomogeneous line broadening. Energy migration occurs over the ${\mathrm{Eu}}^{3+}$ sublattice with quasi-two-dimensional character, via a one-site resonant two-phonon-assisted process.