Add to ORKGThe aim of this lecture is to present the second-order necessary and suf-ficient conditions for vector optimization problems. Our results generalize some of previously obtained results ([BP1, BP2, BZ, GGR]) concerning both scalar and vector optimization problems. Main result: Let f: Rm 7 → Rn be a function minimized with respect to the pointed closed convex cone C with intC 6 = ∅, which is continuous near x ∈ Rm and `−stable at x. Assume that 4l(x) = {ξ ∈ C ′∩SRn; f `(x;h)(ξ) = 0, ∀h ∈ SRm} 6 = ∅, and suppose that for each h ∈ Rm one of the following two conditions is satisfied: (i) Limsupt↓0 f(x+th)−f(x