grammatical number - Plural form of titles

I've heard certain titles pluralised in apparently odd ways, such as a Secretary General being Secretaries General when plural, rather than "Secretary Generals" as I'd have guessed, and I'm wondering if there's a rule on this. For example if you were addressing two female Presidents, would is be "Madames President" (multiple females who preside over something) or "Madame Presidents" (multiple Presidents who are female)?

Answer

The general in attorney general, surgeon general, etc., is actually a postpositive adjective (i.e., an adjective that comes after the noun it modifies). The general, therefore, is the adjective general and has nothing to do with the military rank.

Edit: For the plural of Madam President, the plural would be Mesdames Presidents; one is an honorific, one is a title, and both would be pluralized.