The Theory of Relative Identity, as advocated by Peter Geach, 1 may be said to consist of the following two theses (to which I shall refer, after Wiggins, as 'D' and 'R' respectively): D R (1) 'a=b' is an incomplete expression. One should, in order to complete it, say the same what a and b are. A full identity statement is always of the form, 'a = ~ b' (read: a is the same F as b'). Although both a and b are G, it is possible for a to be the same F as b but a different G than b. I.e., a=r b.Ga'Gb" ..,a=~ b can be true. The theory has come under heavy attack. Fred Feldmanfl John Perry, 3 and Jack Nelson 4 reject both D and R. David Wiggins 5 and Leslie Stevenson 6 reject R (but accept D). Douglas Odegard 7 rejects D (but accepts R). In this paper I shall argue that their arguements against the Theory of Relative Identity (henceforth, TRI) are all unsuccessful, and will suggest several new reasons for accepting TRI. There is, however, one slight difference between Geach's TRI and the version I shall defend. Instead of R, I adopt R, Although both a and b are G, it is possible for a to be the same Fas b but a different Hthan b, when (x) (Fx v Hx) ~ (Gx). I.e., a=e b.Ga.Gb. ~a=n b can be true.