Аннотация:We consider an optimal control problem for an autonomous differential inclusion with free terminal time in the situation when there is a set M (“risk zone”) in the state space Rn which is unfavorable due to reasons of safety or instability of the system. Necessary optimality conditions in the form of Clarke’s Hamiltonian inclusion are developed when the risk zone M is an open set. The result involves a nonstandard stationarity condition for the Hamiltonian. As in the case of problems with state constraints, this allows one to get conditions guaranteeing nondegeneracy of the developed necessary optimality conditions.