A recent trend in the industrial applications of robust parameter design is to consider complex systems which are called "systems with dynamic characteristics" in Taguchi's terminology or signal-response systems in this paper. This potentially important tool in quality engineering lacks a solid basis on which to build a rigorous body of theory and methodology. The purpose of this paper is to provide such a basis. We classify signal-response systems into two broad types: measurement systems and multiple target systems. Three issues are then of fundamental importance. First, a proper performance measure needs to be chosen for system optimization, and this choice depends on the type of system. Taguchi's dynamic signal-to-noise ratio is shown to be appropriate for certain measurement systems but not for multiple target systems. Second, there are two strategies for modeling and analyzing data: performance measure modeling and response function modeling. Finally, the proper design of such experiments should take into account the modeling and analysis strategy. The proposed methodology is illustrated with a real experiment on injection molding.