  Within the framework of viscosity solution, we study the relationship between
the maximum principle (MP) in [9] and the dynamic programming principle (DPP)
in [10] for a fully coupled forward-backward stochastic controlled system
(FBSCS) with a nonconvex control domain. For a fully coupled FBSCS, both the
corresponding MP and the corresponding Hamilton-Jacobi-Bellman (HJB) equation
combine an algebra equation respectively. So this relationship becomes more
complicated and almost no work involves this issue. With the help of a new
decoupling technique, we obtain the desirable estimates for the fully coupled
forward-backward variational equations and establish the relationship.
Furthermore, for the smooth case, we discover the connection between the
derivatives of the solution to the algebra equation and some terms in the first
and second-order adjoint equations. Finally, we study the local case under the
monotonicity conditions as in [14,27] and obtain the relationship between the
MP in [27] and the DPP in [14].
