The invention relates to polymers containing N-substituted maleimide units, to a positive- or negative-working radiation-sensitive mixture comprising a) a polymeric binder which is insoluble in water, but soluble in aqueous-alkaline solutions, and b) at least one radiation-sensitive compound, where the binder comprises a polymer containing N-substituted maleimide units of the formula (I) The invention furthermore relates to a recording material having a support and a radiation-sensitive layer, where the layer includes the mixture. The recording material is particularly suitable for the production of chemical-resistant relief recordings. The planographic printing plates produced from the recording material allow long print runs and are resistant to processing chemicals.