One inherent weakness of traditional reliability theory (see eqr 340) is that the system and the components are always described just as functioning or failed. The first attempts to replace this by a theory for multistate systems of multistate components were made in the late 1970s. By the mid 1980s the basic theory in this area was established. The objective of this article is to introduce concepts of multistate systems and present some upper and lower bounds for the availabilities and unavailabilities, to any level, in a fixed time interval. A series of applications of multistate reliability theory have been suggested during the last years. For example, the theory enables one to consider applications in electrical power generation systems, where the system state is the amount of power generated by the system or in offshore gas pipeline networks where the system state is the amount of gas delivered.