Abstract: An inevitable collision state for a robotic system can be dened as a state for which, no matter what the future trajectory followed by the system is, a collision with an obstacle eventually occurs. An inevitable collision state takes into account both the dynamics of the system and the obstacles, xed or moving. The main contribution of this paper is to lay down and explore this novel concept (and the companion concept of inevitable collision obstacle). Formal denitions of the inevitable collision states and obstacles are given. Properties fundamental for their characterisation are established. This concept is very general and can be useful both for navigation and motion planning purposes (for its own safety, a robotic system should never nd itself in an inevitable collision state!). The interest of this concept is illustrated by a safe motion planning example.