Let $kappa$ be a real abelian field of conductor f and $kappa$(sub)$infty$ = ∪(sub)n$geq$0$kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$geq$0, let G(sub)m,n be the Galois group Gal($kappa$(sub)m/$kappa$(sub)n) and C(sub)m be the group of circular units of $kappa$(sub)m. Let l be the number of prime ideals of $kappa$ above p. Then, for mm>n$geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).