A new 3D, spin-state-selective coherence transfer NMR experiment is described that yields accurate measurements for eight scalar or dipolar couplings within a spin system composed of a methylene adjacent to a methine group. Implementations of the experiment have been optimized for proteins and for nucleic acids. The experiments are demonstrated for Cbeta-Calpha moieties of the third IgG-binding domain from Streptococcal Protein G (GB3) and for C5'-C4' groups in a 24-nt RNA oligomer. Chemical shifts of Calpha, Cbeta and Hbeta (respectively C4', C5' and H5') are dispersed in the three orthogonal dimensions, and the absence of heteronuclear decoupling leads to distinct and well-resolved E.COSY multiplet patterns. In an isotropic sample, the E.COSY displacements correspond to 1J(CalphaHalpha), 2J(CalphaHbeta2)+2J(CalphaHbeta3), 2J(CbetaHalpha), 1J(CbetaHbeta2)+1J(CbetaHbeta3), 1J(CbetaHbeta2)-2J(Hbeta2Hbeta3), 1J(CbetaHbeta3)-2J(Hbeta2Hbeta3), 3J(HalphaHbeta2) and 3J(HalphaHbeta3) for proteins, and 1J(C4'H4'), 2J(C4'H5')+2J(C4'H5"), 2J(C5'H4'), 1J(C5'H5')+1J(C5'H5"), 1J(C5'H5')-2J(H5'H5"), 1J(C5'H5")-2J(H5'H5"), 3J(H4'H5') and 3J(H4'H5") in nucleic acids. The experiment, based on relaxation-optimized spectroscopy, yields best results when applied to residues where the methine-methylene group corresponds to a reasonably isolated spin system, as applies for C, F, Y, W, D, N and H residues in proteins, or the C5'-C4' groups in nucleic acids. Splittings can be measured under either isotropic or weakly aligned conditions, yielding valuable structural information both through the 3J couplings and the one-, two- and three-bond dipolar interactions. Dipolar couplings for 10 out of 13 sidechains in GB3 are found to be in excellent agreement with its X-ray structure, whereas one residue adopts a different backbone geometry, and two residues are subject to extensive chi1 rotamer averaging. The abundance of dipolar couplings can also yield stereospecific assignments of the non-equivalent methylene protons. For the RNA oligomer, dipolar data yielded stereospecific assignments for six out of the eight C5'H2 groups in the loop region of the oligomer, in all cases confirmed by 1J(C5'H5')>1J(C5'H5"), and H5' resonating downfield of H5".