A method for operating an internal combustion engine (1), in particular a marine diesel engine operating with heavy oil, wherein the internal combustion engine(1) has a combustion motor (2) for combustion of fuel and an exhaust gas after-treatment system (3) arranged behind the combustion motor (2); the exhaust gas after-treatment system is used for purifying exhaust gas generated at the time of combustion of a fuel in the case of using a reducing agent and / or an absorbent; and wherein, depending on the cost of the fuel to be combusted in the combustion motor (2) and in accordance with the cost of the reducing agent and / or the absorber to be used in the exhaust after-treatment system (3) in an operating point where the combustion engine (1) is operated and the minimum operating medium cost of fuel and reducing agent and / or absorbent is generated.