One type of stability of the lexicographic set in a vector trajectorial problem with partial criteria of the form MINSUM, MINMAX, and MINMIN in arbitrary combination is investigated.This research was partially supported by DAAD, Fundamental Researches Foundation of Belarus, and International Soros Science Education Program.As usual, we say that a combinatorial lexicographic optimization problem is stable under perturbations of the vector criterion if new lexicographic optima do not appear under small perturbations of parameters of the vector criterion (see, for example, [1,2]). When we weaken this condition, we arrive at the concept of the strong stability, which means that new lexicographic optimal trajectories can appear but, under any small perturbation, there exists a lexicographic optimal trajectory that preserves the lexicographic optimality. Note that the notion of the strong stability radius was introduced by V. K. Leontiev for the linear single-criterion trajectorial problems in [3].In this paper we consider a vector trajectorial problem of lexicographic optimization with partial criteria of the types MINSUM, MINMAX, and MINMIN. Sufficient and necessary conditions of the strong stability of this problem are given. Lower attainable bounds for the strong stability radius are found for the case where /«»-norm is defined in the space of the vector criterion parameters.Let (£, T) be a system of subsets; E = (e\, e 2 ,...,e m }> m > 1; T C 2 E \ {0}, \T\ > 1, i.e., T is some aggregate of non-empty subsets (trajectories) of the set E.On the set E, we define a vector function a(e) = (ai(e),02(e\... ,a n (e}} € R", n > 1, and, on the set Γ, we define a vector criterion