The invention provides an interlock system whereby operation of a domestic appliance such as a food processor containing an electric motor capable of driving a bladed or similar processing tool at relatively high speed is inhibited unless a vessel having a first or a second base configuration is securely mounted to the appliance so as to contain the tool; the vessel having a lid or cover intended to be in place for safe operation when the processing tool is driven by the motor. A vessel-supporting surface of the appliance carries several up-standing latches, each of which is formed with features capable of co-operating with vessels having either of the base configurations to temporarily latch either type of vessel operationally to the appliance. At least one of the latches is formed with first and second apertures allowing operational access for respective interlock actuators responsive to the lid or cover of a vessel being in place as intended, to an interlock switch whereby electrical current is permitted to flow to the motor only when a vessel having one or other of the different base configurations is latched to the appliance and the vessel is safely closed by its lid or cover.