We extend fluorescence correlation spectroscopy to systems that undergo translation or laminar flow in a sample cell. We include theoretical and experimental results; we consider uniform and nonuniform velocity profiles. Concentration correlation analysis extracts microscopic rate parameters from measurements of the spontaneous concentration fluctutations, which occur even at equilibrium. Fluorescence is one of the most sensitive means of monitoring these fluctuations. Analysis of flowing or translating systems (1) offers a method of measuring number concentrations of selected species, for example, of aggregates or polymers, (2) provides a nonperturbing velocity probe, (3) sometimes allows one to circumvent photolytic degradation, (4) has proved extremely helpful in testing and aliging apparatus for fluorescence correaltion measurement and in verifying theoretical analyses, and (5) may be required for interpretation of results obtained on systems in motion, even though that motion is undesired or initially unsuspected. We include both theoretical and experimental results for combined Poiseuille flow and diffusion in the geometry which is of most practical interest. Theoretical expressions for the much simpler cases of nondiffusive Poiseuille flow as well as uniform flow or translation with or without diffusion constitute limiting cases which are displayed explicitly.