In a graphics processing system, when a fragment reaches a texturing stage, it is determined whether the texture to be applied is a static or dynamic texture. If it is determined that the required texels relate to a dynamic texture, then the system first tries to fetch those texels from a dynamic texture memory. If it is found that the texels are not available in the dynamic texture memory, then the relevant texels are generated in an “on-demand” fashion and stored in the dynamic texture memory so that they can be applied to the fragment.