  In gravitational theories involving higher curvature corrections the metric
describes additional degrees of freedom beyond the graviton. Holographic
duality maps these to operators in the dual CFT. We identify infinite families
of theories for which these new modes cannot be truncated and the usual
Fefferman-Graham expansion needs to be modified. New massive gravity in three
dimensions and critical gravity in four dimensions are particular
representatives of these families. We propose modified expansion, study the
near-boundary behaviour of the metric and derive fall-off properties of the
additional modes in theories involving higher derivative corrections.
