  We consider non-linear gravitational models with a multidimensional warped
product geometry. Particular attention is payed to models with quadratic scalar
curvature terms. It is shown that for certain parameter ranges, the extra
dimensions are stabilized if the internal spaces have negative constant
curvature. In this case, the 4-dimensional effective cosmological constant as
well as the bulk cosmological constant become negative. As a consequence, the
homogeneous and isotropic external space is asymptotically AdS. The connection
between the D-dimensional and the 4-dimensional fundamental mass scales sets a
restriction on the parameters of the considered non-linear models.
