  The aim of this article is to study deformation theory of trianguline B-pairs
for any p-adic field. For benign B-pairs, a special good class of trianguline
B-pairs, we prove a main theorem concerning tangent spaces of these deformation
spaces. These are generalizations of Bellaiche-Chenevier's and Chenevier's
works in the case of K=Q_p, where they used (phi,Gamma)-modules over Robba ring
instead of using B-pairs. The main theorem, the author hopes, will play crucial
roles in some problems of Zariski density of modular points or of crystalline
points in deformation spaces of global or local p-adic Galois representations.
