Systematic study on crystal chemistry of Sr2MnGaO 5+δ layered perovskites upon variation of anion stoichiometry and the Mn oxidation state (VMn) was performed. Starting from fully oxygenated Sr2MnGaO5.5 compound, the samples with +3 ≤ VMn ≤ +4 were prepared either by a reduction of oxygen content at controlled partial oxygen pressure or by a partial replacement of oxygen by fluorine. Varying δ is accompanied by structural transformations from Imma (0.03 ≤, δ ≤ 0.13, a ≈ c ≈ √2ap, b ≈ 4ap) to Bmmm (0.41 ≤ δ ≤ 0.46, a ≈ c ≈ √2ap, b ≈ 2ap) and to tetragonal P4/mmm (δ = 0.505, a ≈ ap, c ≈ 2ap). The tetragonal Sr 2MnGaO5-xF1+x oxyfluorides (a ≈ a p, c ≈ 2ap) were prepared by treatment of Sr 2MnGaO5.5 with XeF2. In the Sr 2MnGaO4.78F1.22 structure the MnO6 octahedra are characterized by two short apical Mn-O distances and four long equatorial ones. This is interpreted as an "apically compressed" Jahn-Teller distortion, in contrast to the "apically elongated" one in Sr2MnGaO5+δ.