Use of at least one specific compound selected from the group consisting of (a) phenols, which are characterized in that they bear precisely one phenolic OH group per aromatic ring, have no alkyloxy substituents in the ortho position to the OH group, and bear no carboxyl in free or anionic form, no -CH 2 -N(CH 3) 2, and no substituents comprising an -NH-NH- group, (b) triphenyl phosphite, triphenylphosphine, p-toluenesulfonic acid or N-isopropyl-N'-phenyl-p-phenylenediamine, and (c) NH-acidic compounds selected from sulfonamides having at least one free H on the amide nitrogen atom; heterocyclic compounds having a ring containing 5 or 6 ring atoms, one of which is the hydrogen-bearing -NH- which establishes the NH acidity and the remaining ring atoms are selected from carbon and/or up to one S, wherein the C and/or S atoms adjacent to the "-NH" bear one or, in the case of S, one or preferably two, oxo groups (=O), wherein the heterocyclic compounds having a ring can be present as single rings or be benzo-fused; and heterocyclic aromatic compounds having 5 or 6 ring atoms, one of which is the hydrogen-bearing N which establishes the NH acidity and the remaining ring atoms are selected from carbon and at least two further N atoms; it being possible to also use mixtures of two or more of said "specific compounds"; in combination with a curing agent system as an accelerator and/or for improving full curing, in particular even at low temperatures for radical polymerizations by means of the curing agent system, wherein the curing agent system comprises (i) at least one aldehyde and/or ketone and at least one primary amine, (ii) at least one aldimine, or (iii) at least one ketimine, or a mixture of two or more of constituents (i) to (iii), and at least one further activator (accelerator) in the form of a metal salt, as an initiator system for a synthetic resin composition containing radically polymerizable compounds. (a) phenols, which are characterized in that they bear precisely one phenolic OH group per aromatic ring, have no alkyloxy substituents in the ortho position to the OH group, and bear no carboxyl in free or anionic form, no -CH 2 -N(CH 3) 2, and no substituents comprising an -NH-NH- group, (b) triphenyl phosphite, triphenylphosphine, p-toluenesulfonic acid or N-isopropyl-N'-phenyl-p-phenylenediamine, and (c) NH-acidic compounds selected from sulfonamides having at least one free H on the amide nitrogen atom; heterocyclic compounds having a ring containing 5 or 6 ring atoms, one of which is the hydrogen-bearing -NH- which establishes the NH acidity and the remaining ring atoms are selected from carbon and/or up to one S, wherein the C and/or S atoms adjacent to the "-NH" bear one or, in the case of S, one or preferably two, oxo groups (=O), wherein the heterocyclic compounds having a ring can be present as single rings or be benzo-fused; and heterocyclic aromatic compounds having 5 or 6 ring atoms, one of which is the hydrogen-bearing N which establishes the NH acidity and the remaining ring atoms are selected from carbon and at least two further N atoms; it being possible to also use mixtures of two or more of said "specific compounds"; in combination with a curing agent system as an accelerator and/or for improving full curing, in particular even at low temperatures for radical polymerizations by means of the curing agent system, wherein the curing agent system comprises (i) at least one aldehyde and/or ketone and at least one primary amine, (ii) at least one aldimine, or (iii) at least one ketimine, or a mixture of two or more of constituents (i) to (iii), and at least one further activator (accelerator) in the form of a metal salt, as an initiator system for a synthetic resin composition containing radically polymerizable compounds. it being possible to also use mixtures of two or more of said "specific compounds"; in combination with a curing agent system as an accelerator and/or for improving full curing, in particular even at low temperatures for radical polymerizations by means of the curing agent system, wherein the curing agent system comprises (i) at least one aldehyde and/or ketone and at least one primary amine, (ii) at least one aldimine, or (iii) at least one ketimine, or a mixture of two or more of constituents (i) to (iii), and at least one further activator (accelerator) in the form of a metal salt, as an initiator system for a synthetic resin composition containing radically polymerizable compounds.