  The structure of the Euler-Lagrange equations for a general Lagrangian theory
is studied. For these equations we present a reduction procedure to the
so-called canonical form. In the canonical form the equations are solved with
respect to highest-order derivatives of nongauge coordinates, whereas gauge
coordinates and their derivatives enter in the right hand sides of the
equations as arbitrary functions of time. The reduction procedure reveals
constraints in the Lagrangian formulation of singular systems and, in that
respect, is similar to the Dirac procedure in the Hamiltonian formulation.
Moreover, the reduction procedure allows one to reveal the gauge identities
between the Euler-Lagrange equations. Thus, a constructive way of finding all
the gauge generators within the Lagrangian formulation is presented. At the
same time, it is proven that for local theories all the gauge generators are
local in time operators.
