When performing tile-based rendering a first, pre-pass operation in which primitives in a sequence of primitives for a tile are processed to determine visibility information for the sequence of primitives, the visibility information being usable to determine whether or not fragments for a primitive in the sequence of primitives should subsequently be processed further for the render output, is performed. Thereafter a second, main pass operation is performed in which the further processing of fragments for primitives that were processed during the first, pre-pass operation is controlled based on the determined visibility information for the sequence of primitives, such that for fragments for which the visibility information indicates that the fragments should not be processed further for the render output some or all of the processing during the second, main pass is omitted. The first, pre-pass can be stopped to process primitives in a fail-safe manner if necessary.