Summary: 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 \({\mathcal A}\) which is of the form \({\mathcal A}= C(I, {\mathcal A}_s)\), where \({\mathcal A}_s\) is itself an associative \(*\)-algebra. With an appropriate choice of a \(K\)-cycle over \({\mathcal A}\) it is possible to identify the time-like part of the generalized differential algebra constructed out of \({\mathcal A}\). 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 \({\mathcal A}_s\) of the algebra. Due to this restriction it is 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.