Let G be a (totally) ordered (abelian) group. A G-metric space ( X , ρ ) (X,\rho ) consists of a nonempty set X and a G-metric ρ : X × X → G \rho :X \times X \to G (satisfying the usual axioms of a metric, with G replacing the ordered group of real numbers). That the amalgamation property holds for the class of all metric spaces is attributed, by Morley and Vaught, to Sierpiński. The following theorem is proved. Theorem. The class of all G-metric spaces has the amalgamation property if, and only if, G is either the ordered group of the integers or the ordered group of the reals.