Copolymers having a molecular weight (Mw) of from 10.sup.3 to 10.sup.6, measured by gel-permeation chromatography, that are crosslinkable by acid catalysis and that consist ofa) 100-80 mol. % of structural repeating units of formulae I and II ##STR1## in a ratio of from 1:1 to 1:9 and b) 0-20 mol. % of structural repeating units of formula III ##STR2## wherein X and X' each independently of the other are ##STR3## R is hydrogen or a protecting group that can be removed by the action of acids, the radicals R.sub.1 each independently of the other are C.sub.1 -C.sub.5 alkyl, phenyl or naphthyl or together are 1,2-phenylene or --[C(R.sub.3)(R.sub.4)].sub.x -- wherein R.sub.3 and/or R.sub.4 =hydrogen or methyl and x is from 2 to 5, the radicals R.sub.2 each independently of the other are hydrogen, C.sub.1 -C.sub.5 alkyl or C.sub.1 -C.sub.5 alkoxy, R.sub.5 and R.sub.7 are each hydrogen, R.sub.6 is hydrogen, halogen or methyl and R.sub.8 is hydrogen, halogen, methyl, --CH.sub.2 halogen, --CH.sub.2 CN, --CN, --COOH, --CONH.sub.2, --O--C.sub.1 -C.sub.5 alkyl, --O--CO--C.sub.1 -C.sub.5 alkyl, --COO--C.sub.1 -C.sub.5 alkyl, --COO-phenyl or phenyl, or R.sub.5 and R.sub.6 are each hydrogen and R.sub.7 and R.sub.8 together are --CO--O--CO-- or each independently of the other are --COOH or --COO--C.sub.1 -C.sub.5 alkyl, are described.The said copolymers are suitable, together with compounds that form an acid under actinic radiation, for the production of negative resist systems.