A processing element comprises a plurality of function units (16) operable to execute respective functions in dependence upon received instructions in parallel with one another. An instruction controller includes a plurality of instruction pipelines (42). Each of the pipelines (42) is associated with a function unit (16) of the processing element, and is operable to deliver instructions to the function unit concerned for execution thereby. Each pipeline also includes a timing controller operable to receive timing information for a received instruction, and to determine an initial location in the pipeline into which the instruction is to be loaded, and an instruction handler operable to receive an instruction for the function unit associated with the instruction pipeline concerned, and to load that instruction into the initial location determined by the timing controller.