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Ballester has shown that the problem of deciding whether a Nash stable partition exists in a hedonic game with arbitrary preferences is NP-complete. In this paper we will prove that the problem remains NP-complete even when restricting to additively separable hedonic games.Bogomolnaia and Jackson have shown that a Nash stable partition exists in every additively separable hedonic game with symmetricpreferences. We show that computingNash stable partitions is hard in games with symmetric preferences. To be more specific we show that the problem of deciding whether a non trivialNash stable partition exists in an additively separable hedonic game with non-negativeand symmetricpreferences is NP-complete. The corresponding problem concerning individual stability is also NP-complete since individually stable partitions are Nash stable and vice versa in such games.