A modified superexchange model is used to clarify the physical mechanisms for the formation of nonresonant tunneling conductance in terminated molecular wires. Due to the specific relationship between its key parameters, this model has wider areas of applicability compared to the flat-barrier model and the standard superexchange model, which are widely involved for the physical interpretation of experimental results. Moreover, the results obtained in the two latest models appear in the modified model as characteristic limiting cases. Our estimates show that the exponential decay of conductance, characterized by an attenuation factor β (per repeating unit), is limited by the conditions β ≤ 1.2 and β ≥ 3.7 for the flat-barrier and standard models, respectively. At the same time, the modified superexchange model yields β > 0, which, thus, allows us to analyze the tunneling conductance in molecular wires containing both saturated and conjugated bonds. We also show that for a small number of N repeating wire units (about 3-6 depending on the value of β), the exponential dependence of conductance on N is violated and, accordingly, contact conductance is not identical to conductance at N = 0. Formulas are found which, on the basis of experimental data, make it possible to establish the values of superexchange parameters as well as indicate the conditions of possible hybridization between the orbitals of the anchor groups and the adjacent end units belonging to the interior wire region. One example is the establishment of features in the tunneling conductance of terminated alkane chains caused by the nature of their anchor groups.