Our goal was to study how people understand the negation of counterfactuals (such as “Antonio denied/said that it is false that if Messi had played, then Barcelona would have won”) and semifactuals (such as “Antonio denied that even if Messi had played, Barcelona would have won”). Previous studies have shown that participants negated basic conditionals using small-scope interpretations by endorsing a new conditional with the negated consequent, but also by making large-scope interpretations, endorsing a conjunction with the negated consequent. Three experiments showed that when participants were asked whether the negation of a counterfactual (Experiments 1 and 2) or semifactual (Experiment 3) conditional was followed by a new conditional, they made a small-scope interpretation, endorsing the same conditional with the negated consequent (e.g., “if/even if Messi had played, Barcelona would not have won”). However, they also accepted the conditional with the negated antecedent for semifactuals (e.g., “even if Messi had not played, Barcelona would have won”). When participants were asked whether the negation of a counterfactual or semifactual conditional is followed by a conjunction, they endorsed the conjunction with both the negated antecedent and the consequent (e.g., “Messi did not play and Barcelona did not win”), but again they accepted the conjunction with the negated antecedent only for semifactuals (e.g., “Messi did not play and Barcelona did win”). These results have implications for the main theories of reasoning.