Household appliance arrangement with a household appliance and a communication module, wherein the household appliance arrangement is embodied to set up a wireless data connection between the household appliance and an external communication partner by way of the communication module via at least two different possibilities, for which purpose both the household appliance and the communication module each comprise a wireless data interface, which is embodied to communicate with the other data interface in each case, characterised in that - the communication module comprises a first input facility for inputting an item of information to establish a first wireless data connection between the household appliance and the communication module, wherein the first input facility comprises an identification information input facility for the inputting, by way of a user, of an item of identification information as information for establishing the first wireless data connection, and wherein the communication module comprises a transmission facility for transmitting the input information to the household appliance to establish the first wireless data connection, a receiving facility for receiving an item of initiation information from the household appliance to establish a second wireless data connection and a confirmation facility for manually confirming the received initiation information, and - the household appliance comprises a second input facility for inputting an item of initiation information to establish the second wireless data connection between the household appliance and the communication module, wherein the second input facility is an input button, a menu-controlled activation, a freely allocatable button or a permanently allocated button, wherein the household appliance comprises a transmission facility for transmitting the initiation information to the communication module to establish the second wireless data connection, wherein the household appliance comprises a receiving facility for receiving an item of identification information from the communication module to establish the first wireless data connection, a non-volatile memory with a prestored item of identification information and a comparison facility for comparing the identification information transmitted by the communication module and the prestored identification information, and is embodied, in the case of a positive comparison of both identification numbers, to establish the first wireless data connection without further user input, wherein the household appliance and the communication module are embodied to optionally establish either the first or the second wireless data connection, in order to set up the wireless data connection between the household appliance and the external communication partner by way of the communication module. - the communication module comprises a first input facility for inputting an item of information to establish a first wireless data connection between the household appliance and the communication module, wherein the first input facility comprises an identification information input facility for the inputting, by way of a user, of an item of identification information as information for establishing the first wireless data connection, and wherein the communication module comprises a transmission facility for transmitting the input information to the household appliance to establish the first wireless data connection, a receiving facility for receiving an item of initiation information from the household appliance to establish a second wireless data connection and a confirmation facility for manually confirming the received initiation information, and - the household appliance comprises a second input facility for inputting an item of initiation information to establish the second wireless data connection between the household appliance and the communication module, wherein the second input facility is an input button, a menu-controlled activation, a freely allocatable button or a permanently allocated button, wherein the household appliance comprises a transmission facility for transmitting the initiation information to the communication module to establish the second wireless data connection, wherein the household appliance comprises a receiving facility for receiving an item of identification information from the communication module to establish the first wireless data connection, a non-volatile memory with a prestored item of identification information and a comparison facility for comparing the identification information transmitted by the communication module and the prestored identification information, and is embodied, in the case of a positive comparison of both identification numbers, to establish the first wireless data connection without further user input, wherein the household appliance and the communication module are embodied to optionally establish either the first or the second wireless data connection, in order to set up the wireless data connection between the household appliance and the external communication partner by way of the communication module.