Process for producing a polyisocyanurate plastic, comprising the following steps: a) providing a polyisocyanate composition A) which comprises 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 not more than 20% by weight, b) catalytically trimerizing the polyisocyanate composition A) at a temperature between 0 °C and 80 °C using at least one tertiary organic phosphine catalyst B) of the general formula in which R1, R2 and R3 are identical or different radicals and are each an alkyl or cycloalkyl group having up to 10 carbon atoms, preferably an alkyl group having 2 to 8 carbon atoms or a cycloalkyl group having 3 to 8 carbon atoms, an aralkyl group having 7 to 10 and preferably 7 carbon atoms, or an aryl group which has 6 to 10 and preferably 6 carbon atoms and is optionally substituted by alkyl radicals having up to 10 and preferably 1 to 6 carbon atoms, with the proviso that not more than one of the radicals is an aryl group and at least one of the radicals is an alkyl or cycloalkyl group, or in which R1 and R2 are aliphatic in nature and, joined to one another, together with the phosphorus atom form a heterocyclic ring having 4 to 6 ring members, where R3 is an alkyl group having up to 4 carbon atoms. a) providing a polyisocyanate composition A) which comprises 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 not more than 20% by weight, b) catalytically trimerizing the polyisocyanate composition A) at a temperature between 0 °C and 80 °C using at least one tertiary organic phosphine catalyst B) of the general formula in which R1, R2 and R3 are identical or different radicals and are each an alkyl or cycloalkyl group having up to 10 carbon atoms, preferably an alkyl group having 2 to 8 carbon atoms or a cycloalkyl group having 3 to 8 carbon atoms, an aralkyl group having 7 to 10 and preferably 7 carbon atoms, or an aryl group which has 6 to 10 and preferably 6 carbon atoms and is optionally substituted by alkyl radicals having up to 10 and preferably 1 to 6 carbon atoms, with the proviso that not more than one of the radicals is an aryl group and at least one of the radicals is an alkyl or cycloalkyl group, or in which R1 and R2 are aliphatic in nature and, joined to one another, together with the phosphorus atom form a heterocyclic ring having 4 to 6 ring members, where R3 is an alkyl group having up to 4 carbon atoms. R1, R2 and R3 are identical or different radicals and are each an alkyl or cycloalkyl group having up to 10 carbon atoms, preferably an alkyl group having 2 to 8 carbon atoms or a cycloalkyl group having 3 to 8 carbon atoms, an aralkyl group having 7 to 10 and preferably 7 carbon atoms, or an aryl group which has 6 to 10 and preferably 6 carbon atoms and is optionally substituted by alkyl radicals having up to 10 and preferably 1 to 6 carbon atoms, with the proviso that not more than one of the radicals is an aryl group and at least one of the radicals is an alkyl or cycloalkyl group, or in which R1 and R2 are aliphatic in nature and, joined to one another, together with the phosphorus atom form a heterocyclic ring having 4 to 6 ring members, where R3 is an alkyl group having up to 4 carbon atoms.