It is shown that the stalks of ample Banach bundles inherit (and strengthen in some cases) finite representability of a normed space in “adjacent” stalks. Each of the facts established in the paper can be regarded as an analog of the corresponding property of ultraproducts of Banach spaces.

Keywords:local theory of Banach spaces, ultraproduct of Banach spaces, finite representability of a normed space, ample continuous Banach bundle.