When a processing resource of a data processing system is to perform processing tasks for applications executing on a host processor, the host processor prepares a plurality of command streams to cause the processing resource to perform the processing tasks. When a processing task to be added to a command stream has a dependency on a processing task or tasks that will be included in another command stream, a wait command is added to the command stream that is to include the processing task that has a dependency on a processing task or tasks that will be included in the another command stream, to cause the processing resource to delay executing subsequent commands in the command stream after the wait command, until the processing resource has reached a particular position in the another command stream.