The report is dedicated to generalizations
of Hamiltonian mechanics, which allow us to
include into consideration the so called
"non-Lagrange" systems. The following items
are considered: different deformations of
Poissons brackets; generalized Fedosov
manifolds in the case of non-symplectic
manifolds; the system "charged particle in the
field of magnetic monopole"; formulation of
covariant variational principle; the
construction of variational principle in the
case of inexact symplectic forms.