We consider sixth-order theories of gravity with Lagrangians containin
g the term R(N) square R, where N > 1 is an integer. A conformal trans
formation gives a picture with two scalar fields in Einstein's theory.
We find de Sitter and power law inflationary solutions. However, the
theory has an unstable weak-field behaviour, because the linearized fi
eld equation is of lower order than the non-linear one.