The method of stabilizing mineral oil and its refinery products by addition thereto of a small stabilizing amount of alternating copolymers of the type. . . A -- B -- A -- B -- A . . .in which A denotes the structural unit of the general formula--C(R.sup.1)(R.sup.2) - CH.sub.2 --where R.sup.1 denotes hydrogen or alkyl of from 1 to 8 carbon atoms and R.sup.2 has the meanings stated for R.sup.1 or denotes a phenyl group, and in which B stands for structural units of the general formulae ##STR1## where R.sup.3 denotes a saturated hydrocarbon radical of from 8 to 20 carbon atoms and R.sup.4 denotes hydrogen or alkyl of from 8 to 20 carbon atoms.