Non-linear electrodynamics of a ring-shaped Andreev interferometer (superconductor-normal conductor-superconductor hybrid structure) inductively coupled to a circuit of the dissipative current is investigated. The current-voltage characteristics (CVC) is demonstrated to be a series of loops with several branches intersecting in the CVC origin. The sensitivity of the transport current to a change of the applied external magnetic flux can be comparable to the one of the conventional SQUIDs. Spontaneous arising of coupled non-linear oscillations of the transport current, the Josephson current and the magnetic flux in Andreev interferometers are also predicted and investigated. The frequency of these oscillations can be varied in a wide range, while the maximal frequency can reach $omega_{max} sim 10^{12}$ $sec^{-1}$.
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