The NMR spin-spin coupling constants (SSCCs) across the H-bond in proteins are sensitive to the electronic structure of the H-bonded system, i.e., the N-(HO)-O-...=C group in proteins. The spin-spin coupling mechanism across the H-bond involves a strong electric field effect, steric exchange interactions, and some weak covalent effects (transfer of electronic charge). The electric field effect is reflected by one-orbital contributions to the SSCC and can be tested with the help of probe charges. A negative charge opposite to the N-H bond leads to increased polarization of the N-H bond, a larger contact density at the N nucleus, and a stronger FC coupling mechanism for those SSCCs involving the N nucleus. Similarly, a positive charge opposite to the O=C bond, distorts the O density into the direction of the external charge and in this way decreases the spin density at the O nucleus. All SSCCs across the H-bond depend primarily on the electric field effect and two-orbital steric exchange interactions. The lone pair contributions to the Fermi contact term of (2h)J(ON) (and to a lesser extent (3h)J(CN)) provide a direct measure on possible covalent contributions in the form of charge-transfer interactions. According to calculated charge-transfer values and lone-pair contributions to SSCC (2h)J(ON), the covalent contribution to the H-bond is rather small (less than 15% at 1.9 Angstrom for a bending angle beta(COH) of 120degrees). The zeroth-order density and the spin-spin coupling mechanism, which depends largely on the first-order spin density, both describe the H-bond as being electrostatic rather than covalent. The electric field effect largely determines the geometrical dependence of the SSCCs of a hydrogen-bonded system.