Multimedia presentations are composed of objects belonging to different data types such as video, audio, text and image. An important aspect is that, quite often, the user defining a presentation needs to express sophisticated temporal and spatial constraints among the objects composing the presentation. We present a system (called MPGS-Multimedia Presentation Generator System) which supports the specification of constraints among multimedia objects and the generation of multimedia presentations according to the specified constraints. The constraint model provided by MPGS is very flexible and powerful in terms of the kinds of object constraints it can represent. A large number of innovative features are supported including: asynchronous and simultaneous spatial constraints; components of interest and priority levels; motion functions. Obviously, the flexibility provided to the users requires the development of nontrivial techniques to check constraint consistency and to generate a presentation satisfying the specified constraints. We illustrate the solutions we have devised in the framework of MPGS.