  The concept of Lagrange structure allows one to systematically quantize the
Lagrangian and non-Lagrangian dynamics within the path-integral approach. In
this paper, I show that any Lagrange structure gives rise to a covariant
Poisson brackets on the space of solutions to the classical equations of
motion, be they Lagrangian or not. The brackets generalize the well-known
Peierls' bracket construction and make a bridge between the path-integral and
the deformation quantization of non-Lagrangian dynamics.
