In my view, the moral case for giving animals legal protection is strong. This is so whether or not we think of animals as having moral rights, such as a right to be cared for, or at least a right not to be harmed, because even if animals do not have moral rights, humans have moral duties toward animals, such as a general duty not to harm animals, say, by performing experiments on them, or raising them for food, or having them perform tricks to amuse tourists. The question I wish to consider in this article, however, is not what moral rights animals have, or even what our moral duties to animals are, but whether we have reason to think of animal law not only as imposing legal duties on humans, but also as conferring legal rights on animals. This is not a moral question, but a question about how to conceptualize legal positions, and the arguments in favor of or against competing conceptualizations should be of a theoretical nature. I shall argue (A) that while there are good moral reasons to impose legal duties on humans regarding the treatment of animals, there are good theoretical reasons not to think of animals as legal right-holders, because doing so would either be pointless, on the interest-theory analysis, or else incoherent, on the will-theory analysis. On route to this conclusion, I shall also argue (B) that in the field of law, the method of explication is in many cases, including the elucidation of the concept of a legal right, preferable to conceptual analysis, strictly conceived; (C) that we should think of legal rights as complexes of Hohfeld-elements (claims, liberties, powers, immunities) and distinguish accordingly between claim-rights, liberty-rights, power-rights, and immunity-rights; (D) that when discussing animal rights we should focus on claim-rights; and, finally, (E) that an explication of the concept of a legal right along the lines of the will-theory of legal rights is preferable to an explication along the lines of the interest-theory.