A method for operating a fuel-supply system using a lambda-control apparatus for an internal-combustion engine wherein the amount of fuel to be supplied to the internal combustion engine is a function of signals representing the speed (RPM), the engine load, the exhaust-composition, and the temperature of the exhaust-gas sensor together with the attainment of a given temperature of the engine as an additional control criteria for the lambda-control apparatus. The method further includes deriving a temperature signal from the internal combustion engine to operate a threshold element with a hystereses whose switching values lie at about 10.degree. C. and 50.degree. C. to 85.degree. C. for optimum fuel mixture in the combustion chamber. The output signal of the threshold element can be further utilized for a supplementary warm-up fuel enrichment for better ignition characteristics, engine smoothness, and exhaust gas composition. The apparatus according to the invention has transducers for sensing speed, load, exhaust gas composition and temperature together with a threshold element and a logic element for signals from a sensor in the internal combustion engine so that the lambda-control apparatus can be regulated as a function of the output signal from said logic element.