'asyntactic' originates from Greek elements: the prefix 'a-' meaning 'not' and the adjective 'syntaktikos' (from 'syn-' + 'tassein') meaning 'arranged together'.

'syntaktikos' passed into Late Latin/Latin as 'syntacticus' and into English as 'syntactic'; the modern English form 'asyntactic' was created by adding the negative prefix 'a-' to 'syntactic'.

Initially it signified 'not arranged according to syntax' and it has retained the general meaning of 'lacking or violating syntactic structure' in modern usage.