NMR J-coupling calculations at the second-order of polarization propagator approach, SOPPA, are among the most reliable. They include a high percentage of the total electron correlation effects in saturated and unsaturated molecular systems. Furthermore, J-couplings are quite sensitive to the whole electronic molecular framework. We present in this article the first study of all three response mechanisms, Fermi contact, FC, spin-dipolar, SD and paramagnetic spin orbital, PSO, for J-couplings with occupied localized molecular orbitals at the SOPPA level of approach. Even though SOPPA results are not invariant under unitary transformations, the difference between results obtained with canonical and localized molecular orbitals, LMOs, are small enough to permit its application with confidence. The following small-size saturated and unsaturated compounds were analyzed: CH, CH3F, C2H6, NH3, C2H4, CH2NH, H2C=CHF, and FHC=CHF. The local character of the FC mechanism that appears in J-couplings of these molecular models is shown through the analysis of contributions from LMOs. The importance of including the electron correlation on the engaged bonding orbitals for one-bond couplings is emphasized. Almost all electron correlation effects are included in such orbitals. Interesting findings were the large contributions by s-type LMOs to the C-H and C-C J-couplings; they are responsible for the variation of (1)J(C-C) when going from ethane to ethene and to 1,2-difluoroethene. The previously proposed hyperconjugative transfer mechanism has been tested. Among other tests we found the difference anti-syn of one-bond (1)J(C-H) in imine as due to both the corresponding sigma(C-H) and the lone-pair, LP, contribution. Geminal and vicinal J-couplings were also analyzed. Our findings are in accord with a previous work by Pople and Bothner-by, who considered results taken from calculations or empirical data. For all geminal couplings the pattern of J-couplings, like the change of sign, is originated in the main bondings that participate in the coupling pathways. The finding of asymmetric contributions of LP to vicinal H-H couplings in imine is highlighted. The analysis of J-couplings by contributions from LMOs to the noncontact mechanisms, SD and PSO, show that the pi electronic framework makes both terms grow in the specific case of the model compounds studied here. The PSO mechanism is more efficient when a sigma bond is vicinal to a pi bond. We found in this way an efficient and powerful scheme to get a deeper insight on the electronic molecular framework on which J-couplings are transmitted.