Anaerobically-curing compositions are described comprising (A) a polymerizable monomer; (B) a halogen-containing compound as a first initiator component; (C) an organic thiol as a second initiator component; and (D) an inhibitor of free-radical polymerization. These compositions are particularly suitable as adhesives and may be formulated as thread-locking adhesives, or may be modified by the addition of various modifying polymers to obtain desired properties such as increased viscosities or pressure-sensitive properties.