  We study the one-loop corrections to the four-point function in the Anti de
Sitter space-time for a $\phi^4$ field theory. Our calculation shows the
existence of non-local counterterms which however respect the AdS isometry. Our
arguments are quite general and applicable to other (non-conformal) AdS field
theories. We also explain why calculations in Euclidean and Lorentzian
signatures should differ even at the leading order in non globaly hyperbolic
manifolds.
