Goidelic substrate hypothesis
Hypothesis of non-Indo-European languages 
Ireland was settled, like the rest of northern Europe, after the retreat of the ice sheets c. 9,000 BC. Indo-European languages are usually thought to have been a much later arrival. The language of the inhabitants could have formed a "substrate" to the Celtic tongues of the newcomers, and could have remained in some of the words, placenames, personal names and grammatical constructs of the new Insular Celtic languages.
Suggested non-Indo-European words in Irish 
Gearóid Mac Eoin proposes the following words as deriving from the substrate- Bréife 'ring, loop', Cufar, Cuifre/Cuipre 'kindness', Fafall/Fubhal, Lufe 'feminine', Slife, Strophais 'straw'; and the following placenames- Bréifne, Crufait, Dún Gaifi, Faffand, Grafand, Grafrenn, Life/Mag Liphi, Máfat.
Peter Schrijver submits the following words as deriving from the substrate: partán 'crab', Partraige (ethnonym), (partaing > Lat. parthicus), pattu 'hare', petta 'hare', pell 'horse', pít 'portion of food', pluc '(round) mass', prapp 'rapid', gliomach 'lobster', faochán 'periwinkle', ciotóg 'left hand', bradán 'salmon', scadán 'herring'. In a further study he gives counter-arguments against some criticisms by Graham Isaac.
Ranko Matasović points out that there are words of possibly or probably non-Indo-European origin in other Celtic languages as well; therefore, the substrate may not have been in contact with Primitive Irish but rather with Proto-Celtic. Examples of words found in more than one branch of Celtic but with no obvious cognates outside Celtic include:
- Middle Irish ainder 'young woman', Middle Welsh anneir 'heifer', perhaps Gaulish anderon (possibly connected with Basque andere 'lady, woman')
- Old Irish berr 'short', Middle Welsh byrr 'short', Gaulish Birrus (name)
- Old Irish bran 'raven', Middle Welsh bran 'raven', Gaulish Brano-, sometimes translated as 'crow' (name element, such as Bran Ardchenn, Bran Becc mac Murchado, and Bran the Blessed)
- Middle Irish brocc 'badger', Middle Welsh broch 'badger', Gaulish Broco- (name element) (borrowed into English as brock)
- Old Irish carpat '(war) chariot', Gaulish carpento-, Carbanto-
- Old Irish eó 'salmon', Middle Welsh ehawc 'salmon', Gaulish *esoks (borrowed into Latin as esox)
- Old Irish cuit 'piece', Middle Welsh peth 'thing', Gaulish *pettia (borrowed into Latin as petia and French as pièce)
- Old Irish molt 'wether', Middle Welsh mollt 'ram, wether', Gaulish Moltus (name) and *multon- (borrowed into French as mouton and English as mutton)
- Stephen Oppenheimer, The Origins of the British (pinpoint or page cite needed) (2009).
- Tristram, Hildegard L.C., ed. (26-27 July 2007). The Celtic Languages in Contact. Potsdam University Press. Retrieved 10 December 2012.
- Schrijver, Peter (2000). "Non-Indo-European Surviving in Ireland in the First Millennium AD". Ériu 51: 195–199.
- Schrijver, Peter (2005). "More on Non-Indo-European Surviving in Ireland in the First Millennium AD". Ériu 55. Retrieved 10 December 2012.
- "Words and Proper Names". Bill.celt.dias.ie. Retrieved 2012-02-18.
- Matasović, Ranko (2009). Etymological Dictionary of Proto-Celtic. Leiden: Brill. ISBN 978-90-04-17336-1.