Some general criteria are given for the stability of a system of convex inequalities and then extended to an arbitrary system by the procedure of convex approximation. The stability is understood in the following sense: given a systemxεDG(x)εM, whereDis a subset of a locally convex spaceX, Ma closed convex cone in a locally convex spaceY, Ga mapping fromDtoY, a solution[xbar]is said to be stable if for every neighbourhoodWofxbar;there exists a neighbourhoodVof 0 εYsuch that for any conditinuous mappingA:D→YsatisfyingA(D∩W) ⊂V+Mthe perturbed systemxεDG(x)A(x)εMhas at lease one solution inW; the system is said to be stable if every its solution is stable.