Introduction. The purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi-split real reductive algebraic groups in [27] with their corresponding Artin factors attached by local class field theory [21]. As a consequence, we establish an identity satisfied by certain normalized intertwining operators. It seems to be useful in applications of the trace formula [1, 29]. More precisely, let G be the group of real points of a quasi-split reductive algebraic group over R. Let A be the set of simple roots defined by a fixed minimal parabolic subgroup Po = M0A0U of G. Fix 6 A, and let P = P9 be the corresponding standard parabolic subgroup of G and write P = MAN for its Langlands decomposition. Fix a nondegenerate character x °f U i ^ (a, H{o)) be an irreducible admissible x-gic Banach (in particular x~generic unitary) representation of M (cf. Section 1). Given v G a£, the complex dual of the Lie algebra of A, let I(v,o,0) be the continuously (quasi-unitarily, if o is unitary) induced representation IndP^Ga® e v 9 and let V(v,o,0) be its space (Section 0). Then F ^ a , ^ = Vfoo^O). Now, let W be the Weyl group of Ao in G. Choose w G W such that w(0) A. Let N~ be the unipotent group opposite to N. Define N$ = U C wN~w~ where w is a representative of w in G. For/ G F(^,a,^)00, define