  The non-holonomic deformations of non-local integrable systems belonging to
the Nonlinear Schrodinger family are studied using the Bi-Hamiltonian formalism
as well as the Lax pair method. The non-local equations are first obtained by
symmetry reductions of the variables in the corresponding local systems. The
bi-Hamiltonian structures of these equations are explicitly derived. The
bi-Hamiltonian structures are used to obtain the non-holonomic deformation
following the Kupershmidt ansatz. Further, the same deformation is studied
using the Lax pair approach and several properties of the deformation
discussed. The process is carried out for coupled non-local Nonlinear
Schrodinger and Derivative Nonlinear Schrodinger (Kaup Newell) equations. In
case of the former, an exact equivalence between the deformations obtained
through the bi-Hamiltonian and Lax pair formalisms is indicated
