Stabilization of inter-brane distance is analyzed in 5-dimensional models with higher-order scalar kinetic terms. Equations of motion and boundary conditions for background and for scalar perturbations are presented. Conditions sufficient and (with o
ne exception) necessary for stability are derived and discussed. It is shown that it is possible to construct stable brane configurations even without scalar potentials and cosmological constants. As a byproduct we identify a large class of non-standard boundary conditions for which the Sturm-Liouville operator is hermitian.
A higher order theory of dilaton gravity is constructed as a generalization of the Einstein-Lovelock theory of pure gravity. Its Lagrangian contains terms with higher powers of the Riemann tensor and of the first two derivatives of the dilaton. Never
theless, the resulting equations of motion are quasi-linear in the second derivatives of the metric and of the dilaton. This property is crucial for the existence of brane solutions in the thin wall limit. At each order in derivatives the contribution to the Lagrangian is unique up to an overall normalization. Relations between symmetries of this theory and the O(d,d) symmetry of the string-inspired models are discussed.
