  We study the Hamilton formalism for Connes-Lott models, i.e., for Yang-Mills
theory in non-commutative geometry. The starting point is an associative
$*$-algebra $\cA$ which is of the form $\cA=C(I,\cAs)$ where $\cAs$ is itself a
associative $*$-algebra. With an appropriate choice of a k-cycle over $\cA$ it
is possible to identify the time-like part of the generalized differential
algebra constructed out of $\cA$. We define the non-commutative analogue of
integration on space-like surfaces via the Dixmier trace restricted to the
representation of the space-like part $\cAs$ of the algebra. Due to this
restriction it possible to define the Lagrange function resp. Hamilton function
also for Minkowskian space-time. We identify the phase-space and give a
definition of the Poisson bracket for Yang-Mills theory in non-commutative
geometry. This general formalism is applied to a model on a two-point space and
to a model on Minkowski space-time $\times$ two-point space.
