A stability theorem for the Pexider functional equation (1) is proved. It is an analogue of the classical theorem of Hyers [5] relating to the stability of the Cauchy functional equation. In 1941 D. H. Hyers proved that if f :E -* E' maps a Banach space E into a Banach space E' and satisfies for some e>0 the condition \\f(s + t)-f(s)-f(t)\\^, s, teE, then there exists exactly one mapping l:E->E' such that l(s + t) = l(s) + l(t) and \\f(s) — / ( s ) | | < £ for all s.teE. It was an affirmative answer to a question of S. Ulam [8] concerning the stability of the linear functional equation. Since that time many papers appeared concerning the stability of other functional equations as well as generalizing the Hyers theorem (see, for instance, [1]—[4], [6], [7]). In the present note we shall give another result of such a type; namely, we shall prove the following stability theorem for the Pexider functional equation (1) f(s + t) = g(s) + h(t) with three unknown functions / , g and h. T H E O R E M . Let (S, +) be an abelian semigroup with zero and let Y be a sequentially complete topological vector space over the field Q of ail rational numbers. Assume that V is a non-empty, Q-convex symmetric and bounded subset of Y. If functions f:S-*Y, g.S-*Y and h:S->Y satisfy the condition (2) f(s + t)-g(s)-h(t)eV, s, teV, then there exist functions faiS^Y, g1:S^Y and h1:S-*Y satisfying the equation {I) for all s,tsS and such that f1(s)—f(s)s3seąc\V, g1(s) — g(s)e 4seąćlV and h^s) — h(s)e 4 seqcl V for all seS. In the proof of this theorem a basic role is played by a lemma on the existence of additive selections of subadditive multifunctions due to Z. Gajda and R. Ger. A multifunction F:S->2 is said to be subadditive iff Manuscript received December 7, 1987, and in final form October 24, 1988. AMS (1991) subject classification: 39B72, 39B52. * Filia Politechniki Łódzkiej, ul. Willowa 2, Bielsko-Biała, Poland.