Photocurable addition-polymerizable compositions containing a free-radically-polymerizable monomer and a photoinitiator system containing i) an arylidonium salt, ii) a sensitizing compound, and iii) an electron donor having an oxidation potential that is greater than zero and less than or equal to that of p-dimethyoxybenzene (1.32 volts vs. S.C.E.). The compositions cure rapidly and deeply under ultraviolet or visible light.