The dependences of the tunnel current on the overpotential and bias voltage for a symmetric electrochemical contact involving two redox groups are calculated. The main physical situations involving various combinations of the strengths of the electronic coupling of the redox groups with each other and with the electrodes are considered in detail. The treatment is more rigorous and complete as compared with previous work. In particular, totally adiabatic transitions are discussed and the potential distribution in the tunnel gap is taken into account. It is shown that the system under consideration manifests negative differential resistance and rectification. A new effect is predicted in the current/overpotential dependence, namely the appearance of two maxima. The experimental data of (Tran et al 2006 Faraday Discuss. 131 197) are addressed. It is concluded that they are compatible with the assumption on a strong screening of the electric potential within the tunnel gap.