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Gauge-invariant treatments of general-relativistic higher-order perturbationson generic background spacetime is proposed. After reviewing the generalframework of the second-order gauge-invariant perturbation theory, we show thefact that the linear-order metric perturbation is decomposed intogauge-invariant and gauge-variant parts, which was the important premis of thisgeneral framework. This means that the development the higher-ordergauge-invariant perturbation theory on generic background spacetime ispossible. A remaining issue to be resolve is also disscussed.

General formulation of general-relativistic higher-order gauge-invariant perturbation theory