When carrying out a second, higher level of anti-aliasing such as 8×MSAA, in a graphics processing pipeline 1 configured to “natively” support a first level of anti-aliasing, such as 4×MSAA, the rasterization stage 3, early Z (depth) and stencil test stage 4, late Z (depth) and stencil test stage 7, blending stage 9, and downsampling and writeback (multisample resolve) stage 11 of the graphics processing pipeline 1 process each graphics fragment or pixel that they receive for processing in plural processing passes, each such processing pass processing a sub-set of the sampling points that the fragment represents, but the fragment shader 6 is configured to process each graphics fragment in a processing pass that processes all the sampling points that the fragment represents in parallel, so as to ensure compliance with the desired higher level of multisampled anti-aliasing.