The present paper describes a general structural stability theory for discretized systems. Instabilities are essential constituents of nonlinear structural responses, the computational assessment of which is exclusively based on incremental-iterative (step-wise) numerical techniques, applied to the tangential equation of motion. The paper derives this fundamental equation as first variation of the nonlinear equation of motions in its standard form and its phase transformation. Further, it transforms the principle of virtual work for arbitrary nonlinear (Kelvin-Voigt-) continua into its incremental variant and finally into the consistent tangential equation of motion. Its application then is demonstrated to classes of time-independent and time-dependent, unstable structural responses, all illustrated by several examples.

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