  We consider a real Klein-Gordon field in the Poincar\'e patch of
$(d+1)$-dimensional anti-de Sitter spacetime, PAdS$_{d+1}$, and impose
dynamical boundary condition on the asymptotic boundary of PAdS$_{d+1}$ that
depend explicitly on the second time derivative of the field at the boundary.
These boundary conditions are of generalized Wentzell type. We construct the
Wightman two-point function for the ground state of the Klein-Gordon theory
whenever the parameters of the theory (the field mass, curvature coupling and
boundary condition parameters) render such ground state admissible. In the
cases in which the mass of the Klein-Gordon field and the curvature coupling
term yield an effectively massless theory, we can define a boundary field whose
dynamics are ruled by the dynamical boundary condition and construct, in
addition to the Wightman function for the Klein-Gordon field,
boundary-to-boundary, boundary-to-bulk and bulk-to-boundary propagators.
