The invention relates to a monofunctional or multifunctional acrylated or methacrylated urethane oligomer where said urethane bond is obtained without use of isocyanate and by the carbonate-amine reaction between a cyclic carbonate and a monoamine or polyamine, with subsequently the conversion of the hydroxyls in the β position with respect to the urethane bond into ester-acids by reaction with a cyclic anhydride, which reaction is followed by the conversion of said acid functional groups into acrylated or methacrylated end groups by reaction with a polyepoxide compound in the presence of acrylic or methacrylic acid.The invention also relates to a preparation process. Said oligomer is used as crosslinkable binder for a functionality of at least 2 in coating, molding, leaktightness agent or sealing compositions or, if monofunctional, as macromonomer in polymerizable compositions for the production of grafted polymers.