Forty college students evaluated 80 conditional arguments with respect to both validity and persuasiveness. The arguments were of four types, two valid (modus ponens and modus tollens) and two invalid (involving affirmation of the consequent and denial of the antecedent). Participants were not good at distinguishing between valid and invalid arguments, although they did so better than at chance. Invalid arguments that were considered to be persuasive were almost 3 times as likely to be judged to be valid as were invalid arguments that were considered not to be persuasive. Whether an argument was judged to be persuasive was influenced by several variables, including the argument’s logical status, its believed logical status, whether the conclusion was believed by the evaluator to be a true statement of fact, whether the minor premise alone could be considered to be an adequate basis for judging the conclusion to be true, whether the argument’s conclusion or any of its premises was (or could be considered to be) false, and how the antecedent and consequent of the major premise were related. Various models of reasoning that predict some of the results are discussed, but there is no extant model that fully explains the relationship between the perceived validity and the perceived persuasiveness of conditional arguments.