The present invention relates to novel polyisocyanurate plastics which are obtainable by catalytic trimerization of a polyisocyanate composition A) which contains oligomeric polyisocyanates and is low in monomeric diisocyanates. “Low in monomeric diisocyanates” means that the polyisocyanate composition A) has a content of monomeric diisocyanates of at most 20% by weight. The invention further relates to the use of these polyisocyanurate plastics for production of coatings, films, semi-finished products and mouldings, and to a process for producing polyisocyanurate plastics comprising the following steps: (a) providing a polyisocyanate composition A) which contains oligomeric polyisocyanates and is low in monomeric diisocyanates, “low in monomeric diisocyanates” meaning that the polyisocyanate composition A) has a content of monomeric diisocyanates of at most 20% by weight; (b) catalytically trimerizing the polyisocyanate composition A).