  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. Nevertheless, 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.
