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 C-β-C-α 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 C-α, C-β and H-β (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 (1)J(Cα Hα), (2)J(Cα Hα) + (2)J(Cα Hβ 3), (2)J(Cβ Hα), (1)J(Cβ Hβ 2) + (1)JC(β Hβ 3), (1)J(Cβ Hβ 2)-(2)J(Hβ 2Hβ 3,) (1)J(Cβ Hβ 3)-(2)J(Hβ 2Hβ 3), (3)J(Hα Hβ 2) and (3)J(Hα Hβ 3) for proteins, and (1)J(C4'H4'), (2)JC(4'H5')+2J(C4'H5'), (2)J(C5'H4'), (1)J(C5'H5')+(1)J(C5'H5"), (1)J(C5'H5')-(2)J(H5'H5'), (1)J(C5'H5')-(2)J(H5'H5'), (3)J(H4'H5'), and (3)J(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 (3)J 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 x(1) 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'H-2 groups in the loop region of the oligomer, in all cases confirmed by (1)J(C5'H5')>(1)J(C5'H5"), and H-5' resonating downfield of H-5".