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We prove that every (not necessarily linear nor continuous) 2-local triplehomomorphism from a JBW$^*$-triple into a JB$^*$-triple is linear and a triplehomomorphism. Consequently, every 2-local triple homomorphism from a vonNeumann algebra (respectively, from a JBW$^*$-algebra) into a C$^*$-algebra(respectively, into a JB$^*$-algebra) is linear and a triple homomorphism.

2-local triple homomorphisms on von Neumann algebras and JBW$^*$-triples