We generalize the classical theory of amenable locally compact groups to Kac algebras. Most of the equivalent definitions of amenability are translated into the formalism of Kac algebras and still remain equivalent. Among others, we see that every "group dual" (i.e. symmetric Kac algebra) is amenable. Results on actions of amenable groups on von Neumann algebras are extended as well; this allows us to obtain new properties on group co-actions (i.e. actions of "group duals").