Home automation system comprising: - a control zone that is geographically defined in the space; - at least one mobile terminal adapted to transmit and receive radio-frequency signals in the control zone; - a plurality of domestic electrical appliances (2a, 2b, 2c, 2d, 2e) installed in the control zone, all or some of said appliances being heating and/or air conditioning appliances (2a, 2c, 2e), characterized in that: - each appliance (2a, 2b, 2c, 2d, 2e) integrates a radio-frequency signal transmitter and receiver; - the appliances (2a, 2b, 2c, 2d, 2e) are arranged as a network so as to communicate in order to convey information between them, said conveyed information being commands for controlling the operation of said heating and/or air conditioning appliances, which communication is performed by transmitting and receiving, in the control zone, radio-frequency signals containing said information; - the communication between the appliances (2a, 2b, 2c, 2d, 2e) of the network is initiated in response to the reception, by at least one of the appliances of said network, of a radio-frequency signal transmitted by the mobile terminal in the control zone, which signal contains commands for directly controlling the operation of the heating and/or air conditioning appliances (2a, 2c, 2e) and for adjusting each of the temperatures thereof around a predefined value; - in response to the reception of the radio-frequency signal transmitted by the mobile terminal in the control zone, the first appliance that receives said signal from said mobile terminal: o changes its operating state and adjusts its temperature around the predefined value, when said first appliance is a heating and/or air conditioning appliance; o transmits, in the network, a radio-frequency signal containing commands for controlling the operation of the other appliances; - in response to the reception of the radio-frequency signal transmitted by the first appliance in the network, each one of the other heating and/or air conditioning appliances (2a, 2c, 2e) changes its operating state and adjusts its temperature around the predefined value. - a control zone that is geographically defined in the space; - at least one mobile terminal adapted to transmit and receive radio-frequency signals in the control zone; - a plurality of domestic electrical appliances (2a, 2b, 2c, 2d, 2e) installed in the control zone, all or some of said appliances being heating and/or air conditioning appliances (2a, 2c, 2e), - each appliance (2a, 2b, 2c, 2d, 2e) integrates a radio-frequency signal transmitter and receiver; - the appliances (2a, 2b, 2c, 2d, 2e) are arranged as a network so as to communicate in order to convey information between them, said conveyed information being commands for controlling the operation of said heating and/or air conditioning appliances, which communication is performed by transmitting and receiving, in the control zone, radio-frequency signals containing said information; - the communication between the appliances (2a, 2b, 2c, 2d, 2e) of the network is initiated in response to the reception, by at least one of the appliances of said network, of a radio-frequency signal transmitted by the mobile terminal in the control zone, which signal contains commands for directly controlling the operation of the heating and/or air conditioning appliances (2a, 2c, 2e) and for adjusting each of the temperatures thereof around a predefined value; - in response to the reception of the radio-frequency signal transmitted by the mobile terminal in the control zone, the first appliance that receives said signal from said mobile terminal: o changes its operating state and adjusts its temperature around the predefined value, when said first appliance is a heating and/or air conditioning appliance; o transmits, in the network, a radio-frequency signal containing commands for controlling the operation of the other appliances; o changes its operating state and adjusts its temperature around the predefined value, when said first appliance is a heating and/or air conditioning appliance; o transmits, in the network, a radio-frequency signal containing commands for controlling the operation of the other appliances; - in response to the reception of the radio-frequency signal transmitted by the first appliance in the network, each one of the other heating and/or air conditioning appliances (2a, 2c, 2e) changes its operating state and adjusts its temperature around the predefined value.