The compressibilities of the nitridosilicate SrYb[Si(4)N(7)] and the oxonitridoaluminosilicates MYb[Si(4-x)Al(x)O(x)N(7-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 V(0) = 302.91 (6) A(3), B(0) = 176 (2) GPa and B' = 4.4 (2) for SrYb[Si(4)N(7)]; V(0) = 310.4 (1) A(3), B(0) = 161 (2) GPa and B' = 4.6 (2) for SrYb[Si(4-x)Al(x)O(x)N(7-x)]; and V(0) = 317.3 (5) A(3), B(0) = 168 (2) GPa and B' = 4.7 (2) for BaYb[Si(4-x)Al(x)O(x)N(7-x)]. While the linear compressibilities of the a and c axes of BaYb[Si(4-x)Al(x)O(x)N(7-x)] are very similar up to 30 GPa, distinct differences were observed for SrYb[Si(4)N(7)] and SrYb[Si(4-x)Al(x)O(x)N(7-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.