The identifiability of a linear deterministic differential system in a state space representation is examined. Conditions are given under which the model and the experimentation make it possible to assign unique values to the unknown parameters of the system. In addition to some general results a more thorough analysis is carried out for a class of linear systems called compartmental systems or pool systems, which are widely applied, e.g., in bioscienccs. The analysis must in almost all cases be carried out separately for each model because conditions for parameter uniqueness in the general case could not be derived.