The invention relates to moldable, radically polymerizable multicomponent mixtures, which may even be present in the form of storable multicomponent systems, containingethylenically unsaturated, polymerizable compounds, if desired in admixture with soluble and/or insoluble fillers and/or other auxiliaries, andan activator system initiatable by contact with oxygen,characterized in that, in their in-use form, the multi-component mixtures are present as at leastly slightly thickened material and contain an activator system based on the following principal components which can be initiated by contact with ambient air:N-alkyl-substituted tert.-arylamines containing at least one aliphatic CH bond in the .alpha.-position,metal compounds at least partly soluble in the system to accelerate the drying of unsaturated oils, andweakly acidic carboxylic acids having pK.sub.s values no lower than about 0.9.In their in-use form, the multicomponent mixtures preferably have a minimum viscosity of at least about 50 to 100 mPa.s. The invention also relates to the use of the activator systems of these mutlicomponent mixtures for the time-controlled hardening--with a predeterminable pot-life--of olefinically unsaturated systems by contact with ambient air at room temperature or only moderately elevated temperatures.