When untransformed display lists are used in a tile-based graphics processing system, the processing involved in deriving sub-primitives may need to be performed in both the geometry processing phase and the rasterization phase. To reduce the duplication of this processing, the control stream data for a tile includes sub-primitive indications to indicate which sub-primitives are to be used for rendering a tile. This allows the sub-primitives to be determined efficiently in the rasterization phase based on this information determined in the geometry processing phase. Furthermore, a hierarchical cache system may be used to store a hierarchy of graphics data items used for deriving sub-primitives. If graphics data items for deriving a sub-primitive are stored in the cache, the retrieval of these graphics data items from the cache in the rasterization phase can reduce the amount of processing performed to derive the sub-primitives.