The disclosure is directed to a method for improving the exhaust-gas quality, which is reduced by sulfur influence, in combustion processes with exhaust-gas catalytic converters. In the method, the oxygen storage capability of the catalytic converter is determined and is compared to a threshold value. When there is a drop below the threshold value, the exhaust-gas temperature is increased and/or an exhaust-gas composition, which acts in a reducing manner, is generated forward of the catalytic converter.