The structures of the 3d divalent transition-metal diarsenates M(2)As(2)O(7) (M = Mn, Co, Ni, Zn) can be considered as variants of the monoclinic (C2/m) thortveitite [Sc(2)Si(2)O(7)] structure type with a ≃ 6.7, b ≃ 8.5, c ≃ 4.7 Å, α ≃ 90, β ≃ 102, γ ≃ 90° and Z = 2. Co(2)As(2)O(7) and Ni(2)As(2)O(7) 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. Mn(2)As(2)O(7) undergoes no phase transition and likewise adopts the thortveitite structure type in C2/m. Zn(2)As(2)O(7) 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 Cr(2)P(2)O(7). Besides descriptions of the low-temperature Co(2)As(2)O(7), Ni(2)As(2)O(7) and Zn(2)As(2)O(7) 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(2)As(2)O(7) phases, the quaternary phase (Ni,Co)(2)As(2)O(7) 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)(2)As(2)O(7) can be considered as a solid solution adopting the α-Ni(2)As(2)O(7) structure type. Differences of the two structure models for (Ni,Co)(2)As(2)O(7) are discussed.