  In this paper we discuss singular Lagrangian systems on the framework of
contact geometry. These systems exhibit a dissipative behavior in contrast with
the symplectic scenario. We develop a constraint algorithm similar to the
presymplectic one studied by Gotay and Nester (the geometrization of the
well-known Dirac-Bergman algorithm). We also construct the Hamiltonian
counterpart and prove the equivalence with the Lagrangian side. A Dirac-Jacobi
bracket is constructed similar to the Dirac bracket.
