A maleimide polymer comprises units derived from a maleimide derivative represented by the following general formula (I): ##STR1## where R.sup.1 is a hydrogen atom or a methyl group, and R.sup.2 is an alkyl, alkenyl or aryl group, each of which groups is substituted by at least one organosiloxane group or fluorine atom, or comprises a copolymer of (1) a maleimide derivative represented by the formula (I) but in which R.sup.2 may be hydrogen or any optionally substituted aliphatic hydrocarbon or aryl group with (2) an alkyl or fluoroalkyl methacrylate or an organosiloxy styrene- or organosiloxy-(meth)acrylic acid derivative.The polymer material may be formulated into contact lenses high in oxygen permeability and having good mechanical properties.