A graphics processing system has a rendering space which is divided into tiles. Primitives within the tiles are processed to perform hidden surface removal and to apply texturing to the primitives. The graphics processing system includes a plurality of depth buffers, thereby allowing a processing module to process primitives of one tile by accessing one of the depth buffers while primitive identifiers of another, partially processed tile are stored in another one of the depth buffers. This allows the graphics processing system to have “multiple tiles in flight”, which can increase the efficiency of the graphics processing system.