  A time dependent generalization of the Ginzburg -Landau Lagrangian is
proposed. It contains two terms determining the time dependence and the four
arbitrary scalar functions. Relevant equations, which coincide with equations
following from the suitable Hamiltonian, are derived by a standard variational
technique. These equations determine the energy conservation law and admit
twofold time dependence which leads either to first or to second order time
derivatives in Ginzburg - Landau equations. By introducing the gauge invariant
potentials and choosing the gauge which differs slightly from the classical
Lorentz one, the theory simplifies significantly. The results gained are
discussed and compared to some earlier propositions. The presented approach,
when reduced to a static one, is found to be in perfect agreement with that
reported recently by the Kol\'{a}\v{c}ek group. This indicates indirectly, that
the equation with the first order time derivative seems to be more justified.
