This article presents the results of the testing of the addition of a hydrogen-to-nitrogen-rich natural gas of the Lw group and its influence on the operation of selected gas-fired domestic appliances. The tests were performed on appliances used for the preparation of meals and hot water production for hygienic and heating purposes. The characteristics of the tested gas appliances are also presented. The burners and their controllers, with which the tested appliances were equipped, were adapted for the combustion of Lw natural gas. The tested appliances reflected the most popular designs for domestic gas appliances in their group, used both in Poland and in other European countries. The tested appliances were supplied with nitrogen-rich natural gas of the Lw group, and a mixture of this gas with hydrogen at 13.2% content. The article presents the approximate percentage compositions of the gases used during the tests and their energy parameters. The research was focused on checking the following operating parameters and the safety of the tested appliances: the rated heat input, thermal efficiency, combustion quality, ignition, flame stability, and transfer. The article contains an analysis of the test results, referring, in detail, to the issue of decreasing the heat input of the appliances by lowering the energy parameters of the nitrogen-rich natural gas of the Lw group mixture with a hydrogen addition, and how it influenced the thermal efficiency achieved by the appliances. The conclusions contain an explanation regarding, among other things, how the design of an appliance influences the thermal efficiency achieved by it in relation to the heat input decrease. In the conclusions, on the basis of the research results, answers have been provided to the following questions: (1) Whether the hydrogen addition to the nitrogen-rich natural gas of the Lw group will influence the safe and proper operation of domestic gas appliances; (2) What hydrogen percentage can be added to the nitrogen-rich natural gas of the Lw group in order for the appliances adapted for combusting it to operate safely and effectively, without the need for modifying them?