  The problem of consistent Hamiltonian structure for O(N) nonlinear sigma
model in the presence of five different types of boundary conditions is
considered in detail. For the case of Neumann, Dirichlet and the mixture of
these two types of boundaries, the consistent Poisson brackets are constructed
explicitly, which may be used, e.g. for the construction of current algebras in
the presence of boundary. While for the mixed boundary conditions and the
mixture of mixed and Dirichlet boundary conditions, we prove that there is no
consistent Poisson brackets, showing that the mixed boundary conditions are
incompatible with all nontrivial subgroups of $O((N)$.
