It is shown that after a sudden change of the voltage bias in device "electrode-molecule-electrode", only the hopping current components are able to achieve a great value as compared to the steady current. The effect becomes especially noticeable at asymmetric coupling of the molecule to each electrode. At such asymmetry, the molecule exhibits itself as a molecular diode which is kinetically recharged during the transfer of electrons through a molecule. Just a specific kinetic molecular charging (at switching on the voltage) and discharging (at switching off the voltage) become responsible for a formation of switch-on and switch-off currents.