An olefin-carboxylic acid copolymer, containing at least one free carboxylic acid side group, or a nitrogen compound quaternized with epoxide in the presence of an olefin-carboxylic acid copolymer, containing at least one free carboxylic acid side group, can be used as a fuel additive or lubricant additive. Processes can be used for preparing additives of this kind and fuels and lubricants additized therewith, such as a detergent additive. These additives, fuels, and lubricants can be used for reduction or prevention of deposits in injection systems of direct injection diesel engines, especially in common rail injection systems; for reduction of fuel consumption of direct injection diesel engines, especially of diesel engines with common rail injection systems; and for minimization of power loss in direct injection diesel engines, especially in diesel engines with common rail injection systems. The additives can also be used for gasoline fuels, especially for operation of DISI engines.