Abstract Explicit expressions and symmetry properties are obtained for the vector bracket < r a lr b L, λ| r 1 l 1 r 2 l 2, λ > and for the corresponding transformed wave function of a two-body state. The equivalence between these results and certain expressions appearing in the angularmomentum decomposition of few-body problems is discussed. The rather fundamental role of these brackets and wave functions in few-body problems is pointed out. Further examples are given of their usefulness. In the Brueekner-Hartree-Fock problem they permit the dynamical equations in coordinate or momentum space to be written in forms suitable for numerical calculation. They also make possible the use of arbitrary single-particle wave functions in nuclearstructure calculations, as illustrated in a numerical study of the single-particle spin-orbit splitting in 16O.