  We study the functional class and locality problems in the context of
higher-spin theories and Vasiliev's equations. A locality criterion that is
sufficient to make higher-spin theories well-defined as field theories on
Anti-de-Sitter space is proposed. This criterion identifies admissible
pseudo-local field redefinitions which preserve AdS/CFT correlation functions
as we check in the 3d example. Implications of this analysis for known
higher-spin theories are discussed. We also check that the cubic coupling
coefficients previously fixed in 3d at the action level give the correct CFT
correlation functions upon computing the corresponding Witten diagrams.
