The invention relates to a method for producing a polyisocyanurate composite material, comprising the following steps: a) providing a polyisocyanate composition A) which contains monomer polyisocyanates at an amount of at least 2 wt. %, and b) catalytically trimerising the polyisocyanate composition A) in the presence of at least one fibrous filler material B) and a trimerisation catalyst C), to form the polyisocyanurate composite material, said trimerisation catalyst C) comprising at least one quaternary ammonium salt and/or a metal salt. The invention also relates to polyisocyanurate composite materials that can be obtained according to the claimed method, and to the use of same to produce a component and components consisting of or containing a claimed polyisocyanurate composite material.