Stationary contacts of practical applications under nominal current operation may exhibit nonlinear behaviour. This may be attributed to the microstructures metal-isolator-metal, metal-oxide-metal and metal-gas-metal which are formed on the apparent contacting area, as oxides and other chemical compounds create interfacial layers. Work function changes of the contacting metals can modulate the effective barrier height and width, resulting in a significant change of the crossing resistance in contacts, even during a time interval of one period. Nonlinear behaviour is developed beyond a threshold field value determinated by the voltage drop at the contact. According to the experimental results it becomes evident that at the stage of moderate degradation, tunnelling occurs. An equivalent circuit is proposed which is valid for stationary contacts of practical applications. The theoretic investigation is based upon commonly accepted relations concerning quantum mechanical tunnelling. Between the experimental results and the theoretical ones a satisfactory agreement was found.