This paper axiomatizes Cobb-Douglas preferences under uncertainty. First, we extend the original Trockel (1989)’s axiomatic foundation to a general state space framework based on a strong homotheticity condition, obtaining also the incomplete case a la Bewley (2002). We also show that this key axiom for Cobb-Douglas expected utility speci cation is refuted by the Ellsberg’s uncertainty aversion behavioral pattern. Our main result provides a set of meaning-ful axioms characterizing Cobb-Douglas maxmin expected utility preferences, which lls the gap between the existing axiomatic foundations for maxmin expected utility preferences and its applications to general equilibrium and – nance under unitary relative risk aversion. Finally, we present brie y how to obtain more general representations like the variational case. JEL Classi cation: D81. Keywords: Cobb-Douglas preferences, Expected utility, Ellsberg paradox, Knightian uncertainty, Incomplete preferences, Maxmin expected utility.