Abstract--- The problem of formulation of an equivalent characterization for instability is considered. The necessary part of the Chetaev's theorem on instability is formulated. Using the developed necessary instability conditions, the Anti-control Lyapunov Function (ALF) framework from [1] is extended and the Control Chetaev Function (CCF) concept is proposed as a counterpart of the Control Lyapunov function (CLF) theory. A (bounded) control is designed, which destabilizes a nonlinear system based on CCF, this control design approach can be useful either for generation of an oscillating or chaotic behavior as in [1], or for analysis of norm controllability from [2].