PCT No. PCT/JP78/00022 Sec. 371 Date July 7, 1979 Sec. 102(e) Date July 2, 1979 PCT Filed Nov. 6, 1978 PCT Pub. No. WO79/00284 PCT Pub. Date May 31, 1979A cross-linkable positive-working ionizing radiation-resist or ultraviolet ray- resist polymer composition including: in polymerized form,(a) units derived from a methacrylic acid ester of the formula:CH.sub.2 .dbd.C(CH.sub.3).COOR where R is an alkyl or haloalkyl group having from 1 to 6 carbon atoms, benzyl or cyclohexyl,(b) units derived from a monoolefinically unsaturated carboxylic acid from 3 to 12 carbon atoms and having from 1 to 3 carboxyl groups, and(c) units derived from methacrylic acid chloride.The amount of the units (c) in the polymer composition is such that the number of moles of the units (b), multiplied by the number of the carboxyl group or groups in each of the units (b) ranges from about 1 to about 20% based on the total number of moles of the units (a), (b) and (c); the amount of the units (c) ranges from about 0.05 to about 3.0% by mole based on the total number of moles of the units (a), (b) and (c); and the molar ratio of the units (b), multiplied by the number of the carboxyl groups in each of the units (b), to the units (c) is greater than 2/1 but less than 250/1.