  In this paper, we continue the study of the Davey-Stewartson system which is
one of the most important$(2+1)$ dimensional integrable models. As we showed in
the previous paper, the dDS (dispersionless Davey-Stewartson) system arises
from Hamiltonian vector fields Lax pair. A new hierarchy of compatible PDEs
defining infinitely many symmetries, which is associated with the dDS system,
is defined in this paper. We show that this hierarchy arises from the
commutation condition of a particular series of one-parameter Hamiltonian
vector fields.
