A multitile processing system has an execution unit on each tile, and an interconnect which conducts communications between the tiles according to a bulk synchronous parallel scheme. Each tile performs an on-tile compute phase followed by an intertile exchange phase, where the exchange phase is held back until all tiles in a particular group have completed the compute phase. On completion of the compute phase, each tile generates a synchronisation request and pauses an issue of instructions until it receives a synchronisation acknowledgement. If a tile attains an excepted state, it raises an exception signal and pauses instruction issue until the excepted state has been resolved. However, tiles which are not in the excepted state can continue to perform their on-tile computer phase, and will issue their own synchronisation request in their own normal time frame. Synchronisation acknowledgements will not be received from all of the tiles in the group until the excepted state has been resolved on the tile with the excepted state.