A graphics processing system performs hidden surface removal and texturing/shading on fragments of primitives. The system includes a primary depth buffer (PDB) for storing depth values of resolved fragments, and a secondary depth buffer (SDB) for storing depth values of unresolved fragments. Incoming fragments are depth tested against depth values from either the PDB or the SDB. When a fragment passes a depth test, its depth value is stored in the PDB if it is a resolved fragment (e.g. if it is opaque or translucent), and its depth value is stored in the SDB if it is an unresolved fragment (e.g. if it is a punch through fragment). This provides more opportunities for subsequent opaque objects to overwrite punch through fragments which passed a depth test, thereby reducing unnecessary processing and time which may be spent on fragments which ultimately will not contribute to the final rendered image.