The central question of this article is, Are animals morally responsible for what they do? Answering this question requires a careful, step-by-step argument. In sections 1 and 2, I explain what morality is, and that having a morality means following moral rules or norms. In sections 3 and 4, I argue that some animals show not just regularities in their social behaviour, but can be rightly said to follow social norms. But are the norms they follow also moral norms? In section 5, I contend, referring to the work of Shaun Nichols, that the basic moral competences or capacities are already present in nonhuman primates. Following moral rules or norms is more than just acting in accordance to these norms; it requires being motivated by moral rules. I explain, in section 6, referring to Mark Rowlands, that being capable of moral motivation does not require agency; being a moral subject is sufficient. Contrary to moral agents, moral subjects are not responsible for their behaviour. Stating that there are important similarities between animal moral behaviour and human, unconscious, automatic, habitual behaviour, I examine in section 7 whether humans are responsible for their habitual moral behaviour, and if they are, what then the grounds are for denying that moral animals are responsible for their behaviour. The answer is that humans are responsible for their habitual behaviour if they have the capacity for deliberate intervention. Although animals are capable of intervention in their habitual behaviour, they are not capable of deliberate intervention.