Effectivity frames are introduced as a model of ability in multi-agent systems, i.e. of what groups of agents can achieve by coordinated action in dynamic processes such as extensive games with or without simultaneous moves. Local effectivity is distinguished from different kinds of global and terminal effectivity, respectively what groups of players can maintain throughout and what they can achieve eventually. We provide an example of how effectivity frames can be used to formalize (I) questions about goal achievement and maintenance, (2) the synthesis problem for multi-agent systems, and (3) the interplay between local and global properties of such systems. A modalogic for local and global coalitional effectivity is presented and we show how the three problems mentioned can be translated into this logical framework and solved by standard logical methods.