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We present a general analysis of instabilities and oscillations of the sequential tunneling current in super- lattices, based on the current-voltage characteristic of a single barrier. Our results depend only on the presence of a negative differential resistance region and are independent of the details of the model. We establish general conditions for the existence of a stable oscillatory region of current-voltage characteristic of the superlattice, and for instability leading to current self-oscillation. Our formalism permits a natural connection to standard results of chaos theory. @S0163-1829~99!50520-1#

General analysis of instabilities and oscillations of the sequential tunneling in superlattices