  Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method
for analyzing singular systems, we consider the Hamiltonian formulation of
metric and tetrad gravities in two-dimensional Riemannian spacetime treating
them as constrained higher-derivative theories. The algebraic structure of the
Poisson brackets of the constraints and the corresponding gauge transformations
are investigated in both cases.
