  Nonresonant three-body decays of D and B mesons are studied. It is pointed
out that if heavy meson chiral perturbation theory (HMChPT) is applied to the
heavy-light strong and weak vertices and assumed to be valid over the whole
kinematic region, then the predicted decay rates for nonresonant charmless
3-body B decays will be too large and especially B^- --> pi^- K^+ K^- greatly
exceeds the current experimental limit. This can be understood as chiral
symmetry has been applied there twice beyond its region of validity. If HMChPT
is applied only to the strong vertex and the weak transition is accounted for
by the form factors, the dominant B^* pole contribution to the tree-dominated
direct three-body B decays will become small and the branching ratio will be of
order 10^{-6}. The decay modes B^- --> (K^- h^+ h^-)_{NR} and bar{B}^0 -->
(bar{K}^0 h^+h^-)_{NR} for h = pi, K are penguin dominated. We apply HMChPT in
two different cases to study the direct 3-body D decays and compare the results
with experiment. Theoretical uncertainties are discussed.
