How to ascertain causal relationships has been a key question in science and philosophy for centuries. Based on established principles of causation, we develop a quan- titative measure of an agent’s causal responsibility for the state of a dynamical system: we measure the degree to which an agent’s action has caused the system state at a later point in time as the degree to which the action is necessary and sufficient for this state. Our concept can be applied in deterministic as well as in stochastic systems, and for continuous and discrete conceptions of the system state. We find that the extent of causal responsibility crucially depends on the specifics of system dynamics, type of action and the point in time at which the system state occurs. Quantitatively measuring causation in dynamical systems is relevant for attributing an observed system state to its causes, assessing the effectiveness of management actions and policies, or designing liability regulations. Our concept also provides information about the temporal extent of an agent’s causal efficacy and, hence, the temporal limits of the agent’s normative responsibility.