A system suitable for controlling or tracking the operation of household appliances or computer or entertainment equipment (subsequently appliance), comprising an appliance-specific accessory, which is located in connection with an appliance either as a separate unit or as a portion of the controlled or monitored appliance and which is attachable to an operating energy and/or water supply (4, 11) of the appliance, and which includes connections (3, 9) for sensors monitoring either a user's presence or activity status or an operating environment or wired connections (7, 12) for signals tracking a flow rate of water or energy consumption, and a processor or a control logic for processing information received by way of said connections, and control outputs for controlling (6, 13) the operation or operating energy or water of an appliance, or control signals for local or remote communication, the accessory is configured to monitors 1) the operating status of an appliance connected therewith on the basis of energy consumed thereby (measurement 7) or a water flow rate (measurement 12) or temperature and 2) the signal of an accessory linked functionally with the operating environment of the appliance, such as the signal of a leak, smoke, carbon monoxide, gas or temperature sensor or other operating status related signal or a user's activity status or presence, characterized in_that the appliance-specific accessory of the system is configured to a) independently adapt itself to the signals of both the appliance connected therewith and other accessories or peripheral sensors of the operating environment,_said signals including normal active cycles and consumption of energy or energy and water of the appliance and verification of active presence of a user by monitoring the use of the appliance, and on the basis of said adaptation said appliance-specific accessory is configured to perform a control of the appliance's operating status in such a way that it guides automatically the appliance's energy or water supply or activity (21, 22) to a predetermined operating status, and b) identify signals or inter-signal relationships of the appliance connected therewith and accessories linked with its operating environment, such as peripheral sensors or similar other accessories, by tracking the conditions resulting from a normal or incorrect use or a malfunction of the appliance and, on the basis of such identification, control operation of the appliance and/or the peripherals or to communicates information about said conditions locally or by way of data transfer links from the operating facility to desired parties, whereby the accessory is adapted to prepare a user interface capable of self-control according to ambient conditions and the operating status of the appliance connected therewith. 1) the operating status of an appliance connected therewith on the basis of energy consumed thereby (measurement 7) or a water flow rate (measurement 12) or temperature and 2) the signal of an accessory linked functionally with the operating environment of the appliance, such as the signal of a leak, smoke, carbon monoxide, gas or temperature sensor or other operating status related signal or a user's activity status or presence, a) independently adapt itself to the signals of both the appliance connected therewith and other accessories or peripheral sensors of the operating environment,_said signals including normal active cycles and consumption of energy or energy and water of the appliance and verification of active presence of a user by monitoring the use of the appliance, and on the basis of said adaptation said appliance-specific accessory is configured to perform a control of the appliance's operating status in such a way that it guides automatically the appliance's energy or water supply or activity (21, 22) to a predetermined operating status, and b) identify signals or inter-signal relationships of the appliance connected therewith and accessories linked with its operating environment, such as peripheral sensors or similar other accessories, by tracking the conditions resulting from a normal or incorrect use or a malfunction of the appliance and, on the basis of such identification, control operation of the appliance and/or the peripherals or to communicates information about said conditions locally or by way of data transfer links from the operating facility to desired parties,