The current-voltage (I-V) characteristics and the conductance of a molecular wire are evaluated under the condition of a weak electron-vibrational coupling. It is shown that, in the case of strong couplings between the molecular wire and the electrodes, the current formation is associated with a complicated mixture of superexchange (elastic) and sequential (inelastic) transfer processes just within the molecular wire. At a large energy gap between the level positions of the terminal and interior wire units, the transfer along a sequential electronic pathway becomes noneffective. Therefore, the current is mainly determined by an elastic mechanism. If molecule-electrode couplings are weak, the I-V characteristics are connected with the interfacial charge hopping processes limiting the common charge transmission.