The invention relates 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, where the isocyanurate structure content in the polyisocyanate composition A) is at least 50 mol %, based on the sum total of the oligomeric structures from the group consisting of uretdione, isocyanurate, allophanate, biuret, iminooxadiazinedione and oxadiazinetrione structure that are present in the polyisocyanate composition A); (b) catalytically trimerizing the polyisocyanate composition A), where (i) the catalytic trimerization is conducted at ambient temperatures of at least 80° C.; (ii) the catalytic trimerization is conducted within less than 12 hours at least up to a degree of conversion at which only still not more than 20% of the isocyanate groups originally present in the polyisocyanate composition A) are present. Furthermore, the invention relates to a polyisocyanurate plastic obtainable by the process of the invention, to its use for producing coatings, films, semi-finished products and moldings.