  We study the Hamiltonian formalism for second order and fourth order
nonlinear Schr\"{o}dinger equations. In the case of second order equation, we
consider cubic and logarithmic nonlinearities. Since the Lagrangians generating
these nonlinear equations are degenerate, we follow the Dirac-Bergmann
formalism to construct their corresponding Hamiltonians. In order to obtain
consistent equations of motion, the Dirac-Bergmann formalism imposes some set
of constraints which contribute to the total Hamiltonian along with their
Lagrange multipliers. The order of the Lagrangian degeneracy determines the
number of the primary constraints. Multipliers are determined by the time
consistency of constraints. If a constraint is not a constant of motion, a
secondary constraint is introduced to force the consistency. We show that for
both second order nonlinear Schr\"{o}dinger equations we only have primary
constraints, and the form of nonlinearity does not change the constraint
dynamics of the system. However, introducing a higher order dispersion changes
the constraint dynamics and secondary constraints are needed to construct a
consistent Hamilton equations of motion.
