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The compressibilities of the nitridosilicate SrYb[Si4N7] and the oxonitridoaluminosilicates MYb[Si4− xAl xO xN7− x] ( x = 2; M = Sr, Ba) were investigated by in situ high-pressure X-ray powder diffraction. Pressures up to 42 GPa were generated using the diamond–anvil cell technique. The title compounds are structurally stable to the highest pressure obtained. A fit of a third-order Birch–Murnaghan equation-of-state to the p–V data results in V0 = 302.91 (6) Å3, B0 = 176 (2) GPa and B′ = 4.4 (2) for SrYb[Si4N7]; V0 = 310.4 (1) Å3, B0 = 161 (2) GPa and B′ = 4.6 (2) for SrYb[Si4− xAl xO xN7− x]; and V0 = 317.3 (5) Å3, B0 = 168 (2) GPa and B′ = 4.7 (2) for BaYb[Si4− xAl xO xN7− x]. While the linear compressibilities of the a and c axes of BaYb[Si4− xAl xO xN7− x] are very similar up to 30 GPa, distinct differences were observed for SrYb[Si4N7] and SrYb[Si4− xAl xO xN7− x], with the c axis being the most compressible axis. In all of the investigated compounds the bulk compressibility is dominated by the compression behaviour of the tetrahedral network, while the size of the substituted cation plays a minor role. [ABSTRACT FROM AUTHOR]