The controllability and observability gramians in limited time and frequency intervals are studied, and used for model reduction. In balanced and modal coordinates, a near – optimal reduction procedure is used, vielding the reduction error (norm of the different between the output of the orginal system and the reduced model) almost minimal. Several examples are given to illustrate the concept of model reduction in limited time or/and frequency intervals, for continuous- and discrete-time systems, as well as stable and unstable systems. In modal coordinates, the reduced model obtained from a stable system is always stable. In balanced coordinates it is not necessarily true, and stability conditions for the balanced reduced model are presented. Finally, model reduction is applied to advanced supersonic transport and a flexible truss structure.