Electric field (EF) induced changes of one-bond indirect spin-spin coupling constants are investigated on a wide range of molecules including peptide models. EFs were both externally applied and internally calculated without external EF application by the hybrid density functional theory method. Reliable agreement with experimental data has been obtained for calculated one-bond J-couplings. The role of the EF sign and direction, internal and induced components, hydrogen bonding, internuclear distance and hyperconjugative interactions on the one-bond J-coupling vs EF interconnection is analyzed. A linear dependence of (1)J on EF projection along the bond is obtained, if the bound atoms possess different enough electron densities and an EF determined by the electronic polarization exists along the bond. Accentuating the (1)J(NH) couplings as possible EF sensitive parameters, a systematic study is done in two sets of molecules with a large variation of the native internal EF value. The most EF affected component of the 1JNH coupling constant is the spin-dipole term of Ramsey's formulation; however, in the total J-coupling formation, the EF influence on the Fermi contact term is the most significant. The induced EF projection along the bond is 6.7 times weaker in magnitude than the simulated external uniform field. The absolute EF dependence of the one-bond J-coupling involves only the internal field, which is the sum of the induced field (if the external field exists) and the internuclear field determined by the native polarization. That linear and universal dependence joins the corresponding couplings in a diverse set of molecules under various electrostatic conditions. Many types of the one-bond J-couplings can be potentially measured in biomolecules, and the study of their relation with the electrostatic properties at the corresponding sites opens a new avenue to the full exploitation of the NMR measurable parameters with novel and exciting applications.