A graphics processing apparatus comprises fragment generating circuitry to generate graphics fragments corresponding to graphics primitives, thread processing circuitry to perform threads of processing corresponding to the fragments, and forward kill circuitry to trigger a forward kill operation to prevent further processing of a target thread of processing corresponding to an earlier graphics fragment when the forward kill operation is enabled for the target thread and the earlier graphics fragment is determined to be obscured by one or more later graphics fragments. The thread processing circuitry supports enabling of the forward kill operation for a thread including at least one forward kill blocking instruction having a property indicative that the forward kill operation should be disabled for the given thread, when the thread processing circuitry has not yet reached a portion of the thread including the at least one forward kill blocking instruction.