Abstract. We prove the Hyers-Ulam stability of a Pexiderized exponen-tial equation of mappings f,g,h : G×S → C, where G is an abelian groupand S is a commutative semigroup which is divisible by 2. As an applica-tion we obtain a stability theorem for Pexiderized exponential equationin Schwartz distributions. 1. IntroductionLet f be a map from a vector space (or a semi group) G to the field Cofcomplex numbers satisfying the inequality(1.1) |f ( x + y ) −f ( x ) f ( y ) | ≤ e for all x, y ∈ G. Then f is either bounded or exponential (see [2], [3]).When we consider the above stability problem in the spaces of generalizedfunctions such as the Schwartz tempered distributions, Fourier hyperfunctionswe encounter some stability problem of functional equation with time variablesof positive real numbers while converting given distributional version of thestability problem to classical one. In this paper, we consider the stabilityproblem of Pexiderized exponential equation with time variable(1.2) |f