The invention relates to a beverage machine (1) having an external housing (10) and a movable beverage preparation module (20, 30) that is configured to process a beverage and/or a beverage ingredient to be dispensed. The housing (10) has a front opening (10′) and forms a cavity (10″) for housing the module (20, 30). The module (20, 30) is insertable as a unit into an operative position into the cavity (10″) and removable as a unit out of the cavity (10″) via the front opening (10′). The housing (10) has a cavity connector (11) in the cavity (10″) and the module (20, 30) has a module connector that is connected to the cavity connector (11) when the module (20, 30) is located there against while reaching its operative position and that is disconnected from the cavity connector (11) when the module (20,30) is removed from the cavity (10″). At least one (11) of the connectors has a connection interface device (11a) that is resiliently mounted to a connection base device (11b) to enable a positioning adjustment of the interface device (11a) when the module connector and the cavity connector (11) are connected together.