It is shown that any singular Lagrangian theory: can be formulated without the use of constraints by introducing a Clairaut-type version of the Hamiltonian formalism; leads to a special kind of nonabelian gauge theory which is similar to the Poisson gauge theory; can be treated as the many-time classical dynamics. A generalization of the Legendre transform to the zero Hessian case is done by using the mixed (envelope/general) solution of the multidimensional Clairaut equation. The equations of motion are written in the Hamilton-like form by introducing new antisymmetric brackets. It is shown that any classical degenerate Lagrangian theory is equivalent to the many-time classical dynamics. Finally, the relation between the presented formalism and the Dirac approach to constrained systems is given.

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