  We give a generalization of the Nambu mechanics based on vector Hamiltonians
theory. It is shown that any divergence-free phase flow in $\mathbb{R}^n$ can
be represented as a generalized Nambu mechanics with $n-1$ integral invariants.
For the case when the phase flow in $\mathbb{R}^n$ has $n-3$ or less first
integrals, we introduce the Cartan concept of mechanics. As an example we give
the fifth integral invariant of Euler top.
