The paper proposes a syntactic and semantic analysis of Double Negation (DN). It is shown that there are two types of DN. Strong DN is the result of a Focus construction that involves a polar reading triggered by a Verum Focus; Weak DN, on the other hand, arises when the corresponding n-word is marked as a Contrastive Topic and introduces weak (i.e. non exclusive) alternatives. The paper discusses the occurrence of these two kinds of DN in two types of languages, which feature different negative strategies. While Hungarian is a strict NC language with non-negative n-words and an obligatory negative marker, English and German are non-NC languages, with negative n-words that can function on their own. It is shown that both strong DN and weak DN occur in each of these languages. However, the mechanisms that license n-words contributing the DN reading are different, due to the differences in the nature of the n-words and in the discourse-functional behavior of the languages in question.