Necessary and sufficient conditions for the existence of a simultaneous functional observer for several linear time-invariant (LTI) systems are derived using distinguishability concepts, that generalize the detectability concept for a single system. They generalize also the known results. A structure for common functional observers is proposed, and for two systems, or for several systems without inputs, the problem can be constructively solved. A relationship between the simultaneous observation problem and the existence of unknown input observers is established.