While the oralists see the Odyssey as poem composed by a single oral poet, and the analysts see it as the product of many writers, adding to or changing an original work, the neoanalysts see the Odyssey as a work written by a single author, who, having been trained as an oral poet, reworked and bound together several pre-existing stories into a single epic poem.
The crux of the oralist-neoanalyst debate is as follows: to the oralists, stories or themes that appear in multiple Early Greek Hexameter Poems show that the oral tradition goes beyond epithets, stock phrases and type scenes, to full themes and story-structures. To the neo-analysts, on the other hand, a story or theme appearing in multiple poems is evidence of direct imitation. The precise dating of the various epics is not key, since even if the Iliad and the Odyssey predate the written forms of the cyclic epics, the neoanalysts can argue that the stories told in the cyclic epics are older still. That the poet of the Odyssey was aware of some other pre-existing stories is suggested by his reference to the Argo (XII.70).
Most of the parallels used by the neoanalysts relate not to the Odyssey, but to the Iliad, which is often linked to the cycle-epic the Aethiopis, of which we possess a short summary.
Kullmann, W., 'Oral Poetry Theory and Neoanalysis in Homeric research' GRBS 25 1984 307-23. – The best brief introduction to neoanalyst ideas, by one of neoanalysm’s leading advocates.
Willcock, M. M., 'Neoanalysis' in Morris, I. & Powell, B. (eds.), A New Companion to Homer, Brill, Leiden 1997; pp. 174-189. – A rather more balanced view.
Fenik, B., Typical Battle Scenes in the Iliad, Steiner, Wiesbaden 1968; pp. 231-40 – concludes that neoanalyst findings regarding the Iliad and the Aethiopis do not point to a "simple model-copy relationship between the two poets" but to "a common mythological and stylistic tradition out of which both poems were fashioned."