The reinvestigation of the pseudo-binary systems MBr-BiBr₃ (M = Rb, Cs) revealed two new phases with composition MBi₂Br₇. Both compounds are hygroscopic and show brilliant yellow color. The crystal structures were solved from X-ray single crystal diffraction data. The isostructural compounds adopt a new structure type in the triclinic space group P1 . The lattice parameters are a = 755.68(3) pm, b = 952.56(3) pm, c = 1044.00(4) pm, α = 76.400(2)°, β = 84.590(2)°, γ = 76.652(2)°for RbBi₂Br₇ and a = 758.71(5) pm, b = 958.23(7) pm, c = 1060.24(7) pm, α = 76.194(3)°, β = 83.844(4)°, γ = 76.338(3)°for CsBi₂Br₇. The crystal structures consist of M⁺ cations in anticuboctahedral coordination by bromide ions and bromidobismuthate(III) layers ²_∞[Bi₂Br₇]^-. The 2D layers comprise pairs of BiBr₆ octahedra sharing a common edge. The Bi₂Br₁₀ double octahedra are further connected by common vertices. The bismuth(III) atoms increase their mutual distance in the double octahedra by off-centering so that the BiBr₆ octahedra are distorted. The CsBi₂Br₇ type can be interpreted as a common hexagonal close sphere packing of M and Br atoms, in which 1/4 of the octahedral voids are filled by Bi atoms. The structure type was systematically analyzed and compared with alternative types of common packings. The existence of a compound with the suggested composition CsBiBr₄ could not be verified experimentally.