'non-anthracene-containing' is an English compound formed from the prefix 'non-' (from Latin 'non', meaning 'not'), the chemical name 'anthracene' (from Greek 'άνθραξ' / 'anthrax', meaning 'coal', with the hydrocarbon suffix '-ene'), and the present-participle form of the verb 'contain' (from Latin 'continere', to hold together).

'anthracene' was coined in chemical nomenclature from Greek 'anthrax' (coal) to name a coal-tar-derived hydrocarbon; 'contain' comes from Latin 'continere' → Old French/Middle English forms → modern English 'contain'; combining these elements in English produced the descriptive compound 'non-anthracene-containing'.

Each element has retained a similar sense: 'non-' has long negated terms, 'anthracene' has remained the name of the specific hydrocarbon, and 'contain' has meant 'to hold or include'; together they now mean 'not including anthracene'.