  For finitely generated groups, amenability and F{\o}lner properties are
equivalent. However, contrary to a widespread idea, Kaimanovich showed that
F{\o}lner condition does not imply amenability for discrete measured
equivalence relations. In this paper, we exhibit two examples of $C^\infty$
foliations of closed manifolds that are F{\o}lner and non amenable with respect
to a finite transverse invariant measure and a transverse invariant volume,
respectively. We also prove the equivalence between the two notions when the
foliation is minimal, that is all the leaves are dense, giving a positive
answer to a question of Kaimanovich. The equivalence is stated with respect to
transverse invarian measures or some tangentially smooth measures. The latter
include harmonic measures, and in this case the F{\o}lner condition has to be
replaced by $\eta$-F{\o}lner (where the usual volume is modified by the modular
form $\eta$ of the measure).
