  The lagrangian of N=2, D=6 supergravity coupled to E_7 X SU(2) vector- and
hyper-multiplets is derived. For this purpose the coset manifold E_8/E_7 X
SU(2), parametrized by the scalars of the hypermultiplet, is constructed. A
difference from the case of Sp(n)-matter is pointed out. This model can be
considered as an intermediate step in the compactification of D=10 supergravity
coupled to E_8 X E_8 matter to four-dimensional model of E_6 unification.
