Unambiguous unsteady-state material balances may be. written for systems of arbitrary complexity in terms of boundary fluxes and system contents. Such balances provide a basis for the analysis of tracer experiments even when the residence-time concept is not applicable. Counterparts of the familiar integral relationships for residence-time distributions are derived for the more general situation. Circumstances exist for which residence-time distributions may be properly defined in addition to the usual "closed-closed" case. When a system possesses a residence-time distribution the mean residence time is the ratio of the steady-state tracer holdup to the rate of steady tracer transmission through the system. This result is a more general form of the well-known principle that the mean residence time for steady, constant-density, single-phase flow through a closed system is the ratio of the volume to the volumetric flow rate. Examples illustrate how the general principle permits direct evaluation of the mean residence time by steady-state analysis in the presence of such features as density variation, absorbing boundaries and multiple feeds with diierent compositions. Moreover, the result quoted applies equally to multiphase and reacting systems. When equilibrium obtains in the steady state the mean time is directly related to thermodynamic parameters and transients may be used to determine equilibrium properties without reference to process models. tThis paper is based in part on paper 69d, A.1.Ch.E. 64th National Meeting, San Francisco, November 1971.