[en] Quantum theories of gravity (e.g. string theories) lead to higher derivative terms in the effective gravitational action. We present a general discussion of classical stability for compactification solutions of higher derivative gravity (also applicable for other bosonic fields and in four dimensions). In general there is no need for higher derivative terms to appear as generalized Euler forms. As a specific example we discuss solutions M⁴ x S^D for the most general four-derivative approximation of pure higher dimensional gravity. For a certain range of parameters, instabilities for low momentum fluctuations may be absent. For the allowed parameter range, however, higher poles of propagators appear at momenta only slightly larger than the compactification scale, indicating insufficiency of the four-derivative approximation at this scale. (orig.)