A strong tradition in philosophy denies the possibility of moral dilemmas. Recently, several philosophers reversed this tradition. In this dissertation, I clarify some fundamental issues in this debate, argue for the possibility of moral dilemmas, and determine some implications of this possibility. ;In chapter I, I define moral dilemmas roughly as situations where an agent morally ought to adopt each of two alternatives but cannot adopt both. Moral dilemmas are resolvable if and only if one of the moral oughts overrides (...) the other. ;In chapter II, I criticize several opponents of moral dilemmas, including utilitarians, Kant, Aquinas, and Ross. My main criticism is that no opponent of moral dilemmas can adequately justify moral residue . ;Chapters III and IV concern the two main arguments against the possibility of moral dilemmas. First, the argument for 'ought' implies 'can' runs as follows. If the agent cannot adopt both, then it is not the case that the agent ought to adopt both. But the agent ought to adopt both, since the agent ought to adopt each . Thus, the defining judgements of a moral dilemma seem to imply a contradiction. In response, I argue that the relation between 'ought' and 'can' is not a logical implication but a conversational implicature. ;Chapter IV concerns the argument from 'ought' implies 'permitted': If the agent ought to adopt one alternative, then the agent is permitted to adopt that alternative, which means that it is not the case that the agent ought not to adopt that alternative. But the agent ought not to adopt that alternative, since the agent ought to adopt the other alternative and cannot adopt both. I respond that 'ought' does not logically imply but conversationally implicates 'permitted'. ;In chapter V, I argue that, despite recent claims, both moral realism and anti-realism are compatible with the possibility of moral dilemmas. Thus, there are several reasons to accept and no reasons to deny the possibility of moral dilemmas. (shrink)