Most are pure speculation.

It doesn't seem at all likely from linguistic and historical evidence that it finds its origins in any of the following:

The Scots expression 'och aye', the Greek 'ola kala' meaning 'it is good'.

The Choctaw Indian'oke' or 'okeh' meaning 'it is so'.

The French 'aux Cayes' which means from 'from Cayes', a port in Haiti with a reputation for good rum.

'au quai' meaning 'to the quay', supposedly used by French-speaking dockers.

Or even the initials of a railway freight agent called Obediah Kelly, who is said to have written them on documents he had checked.

A more likely explanation is that the term originated as an abbreviation of 'orl korrekt', a jokey misspelling of 'all correct', which was current in the US in the 1830s.

The oldest known written references to 'OK' result from its use as a slogan by the Democratic Party during the American presidential election of 1840.

Their candidate, President Martin Van Buren was nicknamed Old Kinderhook, after his birthplace in New York State, and his supporters formed the 'OK club'.

This undoubtedly helped popularize the term, although it did not get president Van Buren re-elected.

The only other theory with at least a degree of plausibility, is that the term originated amongst black slaves of West African origin and represents a word meaning 'all right, yes indeed' in various West African languages.

Unfortunately, historical evidence enabling the origin of this expression to be finally and firmly established, is hard to unearth.