A process for the preparation of 2,2-dimethyl-3-arylcyclopropanecarboxylic acid or ester of the formula ##STR1## in which Ar is naphthyl or the radical ##STR2## R.sup.1 is H or C.sub.1 -C.sub.4 -alkyl, Z is oxygen, sulphur, or 1,2-ethenediyl, andR.sup.2 represents hydrogen, halogen, cyano, nitro or trialkylsilyl or a radical, which is optionally substituted by halogen, from the series comprising alkyl, cycloalkyl, alkenyl, alkoxy, alkylenedioxy, alkylthio, alkylsulphinyl, alkylsulphonyl, dialkylamino, phenyl and phenoxy,comprising reacting a 1-aryl-1-halogeno-2,2-dimethyl-3-butanone of the formula ##STR3## in which X.sup.1 is chlorine or bromine, with a base in the presence of a diluent at a temperature between about -20.degree. and +150.degree. C., thereby to form a 2,2-dimethyl-3-arylcyclobutanone of the formula ##STR4## and reacting such 2,2-dimethyl-3-arylcyclobutanone with chlorine or bromine in the presence of an inert diluent at a temperature between about -30.degree. and +50.degree. C., reacting such 2,2-dimethyl-3-arylcyclobutanone with chlorine or bromine in the presence of an inert diluent at a temperature between about -30.degree. and +150.degree. C., thereby to form a 2,2-dimethyl-3-aryl-4-halogenocyclobutanone of the formula ##STR5## and reacting such 2,2-dimethyl-3-aryl-4-halogenocyclobutanone with an alkali metal alcoholate in the presence of an organic solvent or with an alkali metal or alkaline earth metal hydroxide or carbonate in the presence of water and an organic solvent, at a temperature between about -20.degree. and +100.degree. C. The various intermediates are new and the end product is a known intermediate for known insecticides.