Also means
sole
Usage Note
Exclusivo can mean both 'exclusive' in the luxury sense and 'sole/only' (derechos exclusivos = exclusive rights). It is a false friend for English 'exclusive' only partially: in Spanish it does not carry the social 'members-only' connotation as strongly as in English. The adverb exclusivamente means 'exclusively' or 'solely'.
Examples
"Tienen un acuerdo exclusivo con esa empresa."
Natural Translation
They have an exclusive agreement with that company.

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