The notion of local linking is extended to case where the Banach space is decomposed into a direct sum of two infinite dimensional linear subspaces [see H. Brezis and L. Nirenberg, Commun. Pure Appl. Math. 44, No. 8/9, 939-963 (1991; Zbl 0751.58006)]. Some existence theorems for nontrivial critical points of functionals with a local linking at 0 are extended. Applications to elliptic BVP and to Hamiltonian systems are given.