Georg Autenrieth, A Homeric Dictionary

οὐδέ : (but not), and not, nor, not even; never a correlative word, but always (except when meaning ‘but not’) adding a new negation after a previous one expressed or implied; if οὐδέ occurs at the beginning of several successive clauses, the first one refers to some previous negation just as much as the 2d or the 3d, Τηλέμαχ̓, οὐδ᾽ ὄπιθεν κακὸς ἔσσεαι οὐδ̓ ἀνοήμων, not even in the future, i. e. even as not in the past, Od. 2.270 . οὐδὲ γὰρ οὐδέ, doubled for emphasis, no, not at all, Il. 5.22, etc. (When the meaning is ‘but not,’ it would be well to write οὐ δέ separately, as this usage is essentially different from the other one. See μηδέ.)