The structures of the 3d divalent transition-metal diarsenates M
2As2O7 (M = Mn, Co, Ni, Zn) can be considered as variants of the monoclinic (C2/m) thortveitite [Sc2Si2O7] structure type with a ≃ 6.7, b ≃ 8.5, c ≃ 4.7 Å, α ≃ 90, β ≃ 102, γ ≃ 90° and Z = 2. Co2As2O7 and Ni2As2O7 are dimorphic. Their high-temperature (β) polymorphs adopt the thortveitite aristotype structure in C2/m, whereas their low-temperature (α) polymorphs are hettotypes and crystallize with larger unit cells in the triclinic crystal system in space groups P\bar 1 and P1, respectively. Mn2As2O7 undergoes no phase transition and likewise adopts the thortveitite structure type in C2/m. Zn2As2O7 has an incommensurately modulated crystal structure [C2/m(α,0,γ)0s] with q = [0.3190 (1), 0, 0.3717 (1)] at ambient conditions and transforms reversibly to a commensurately modulated structure with Z = 12 (I2/c) below 273 K. The Zn phase resembles the structures and phase transitions of Cr2P2O7. Besides descriptions of the low-temperature Co2As2O7, Ni2As2O7 and Zn2As2O7 structures as five-, three- and sixfold superstructures of the thortveitite-type basic structure, the superspace approach can also be applied to descriptions of all the commensurate structures. In addition to the ternary M
2As2O7 phases, the quaternary phase (Ni,Co)2As2O7 was prepared and structurally characterized. In contrast to the previously published crystal structure of the mineral petewilliamsite, which has the same idealized formula and has been described as a 15-fold superstructure of the thortveitite-type basic structure in space group C2, synthetic (Ni,Co)2As2O7 can be considered as a solid solution adopting the α-Ni2As2O7 structure type. Differences of the two structure models for (Ni,Co)2As2O7 are discussed.