In known water heaters of the generic type, the NOx concentration in the combustion gases is reduced by the arrangement of cooling bars downstream of the burner openings. This measure does not however lead to the desired success in all cases. With the design of the water heater according to the invention, the staying time of the hot combustion gases in the burn-out section (18) is shortened and thereby the formation of NOx in the combustion gases counteracted. The residual content of CO is reduced to a permissible value by an oxidation-type catalytic converter (24) arranged downstream of the first heat exchanger (20). Preferred applications are gas-fired water heaters for hot-water heating systems and/or domestic hot water provision. <IMAGE>