Is the concept of "person" a substance-concept (i.e. a sortal which determines the primitive mode of being for the entities falling under it), or a phased-sortal (a sortal such that its instance need not fall under it throughout its existence)? Recently some philosophers opposing to the traditional view maintain that we are not always persons and that what determines our identity-criterion fundamentally is the biological concept of "human animal". In this paper I argue that this "Animalist" conception is unsound and that the primitiveness of our animal nature should not exclude the concept of "person" as our substance-concept. I suggest, however, that "person" as a genuine substance-concept requires a fresh understanding, foreign to the traditional definition in terms of a set of certain psychological attributes.