There are two main competing schemata of categorisation of Celtic languages. The older P-Celtic/Q-Celtic hypothesis links Gaulish with Brythonic as P-Celtic and links Goidelic with Celtiberian as Q-Celtic. The difference between P and Q languages is the treatment of Proto-Celtic *k^w, which became *p in the P-Celtic languages but *k in Goidelic. For example the word for head is pen in Brythonic languages but ceann in Goidelic; the word for son is mab (earlier map) in Brythonic but mac in Goidelic – maqq on the Primitive Irish Ogham inscriptions.

The other scheme, defended for example by McCone (1996), links Goidelic and Brythonic together as an Insular Celtic branch, as opposed to Continental Celtic languages including Gaulish and Celtiberian.

P-Celtic incorporates the following:

• Gallic
  • Gaulish
  • Lepontic
  • Noric
  • Galatian
• Pritennic
  • Pictish
• Brythonic (British)
  • West Brythonic
    • Old Welsh
      • Middle Welsh
        • Welsh
    • Cumbric
  • Southwestern Brythonic
    • Old Breton
      • Middle Breton
        • Breton
    • Old Cornish
      • Middle Cornish
        • Cornish

Q-Celtic incorporates the following:

• Goidelic
  • Primitive Irish
    • Old Irish
      • Middle Irish
        • Irish
        • Scottish Gaelic
        • Manx
• Celtiberian