  We compare the metric and the Palatini formalism to obtain the Einstein
equations in the presence of higher-order curvature corrections that consist of
contractions of the Riemann tensor, but not of its derivatives. We find that in
general the two formalisms are not equivalent and that the set of solutions of
the Palatini equations is a non-trivial subset of the solutions of the metric
equations. However we also argue that for Lovelock gravities, the equivalence
of the two formalism holds completely and give an explanation of why it holds
precisely for these theories.
