Bipartite systems form a subclass of min-max-plus systems, the latter are characterized by the operations maximization, minimization and addition. Such systems are nonlinear in both the linear classes of max-plus systems and min-plus systems. Structural and nonstructural fixedpoints will be defined and properties pertaining to them will be derived. Bipartite systems can be thought of to be built up from more elementary subsystems ('molecules'). The decomposition into such elementary subsystems will be studied and also how properties of the 'total' system depend on properties of these subsystems. Some counterexamples to some conjectures in an earlier paper on bipartite systems will be given as well.