Carboxylic esters of the formula IR.sup.1 --CO--O--R.sup.2 I,whereR.sup.1 is an aliphatic, straight-chain or branched hydrocarbon radical having alkyl side chains and a number average molecular weight of from 250 to 5000 andR.sup.2 is a straight-chain or branched hydrocarbon radical of 1 to 30 carbon atoms or a radical of the formula II ##STR1## where R.sup.3, R.sup.4, R.sup.5 and R.sup.6, independently of one another, are each hyrogen, branched or straight-chain alkyl, an aromatic radical or an araliphatic radical which may also contain heteroatoms,R.sup.7 and R.sup.8, independently of one another, are each branched or straight-chain alkyl or an aromatic or araliphatic radical which may also contain heteroatoms,X is O, S, NR.sup.9 or PR.sup.9, where R.sup.9 is an aliphatic or aromatic radical,n and m, independently of one another, are each from 2 to 20, andx is from 0 to 30,are used as fuel additives or lubricant additives, and fuel compositions or lubricant compositions contain these additives. Carboxylic acids or carboxylic esters are prepared by reacting polymers having at least 30 carbon atoms and at least one carbon--carbon double bond with carbon monoxide and water or an alcohol.