The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 <latex>$\mu$</latex> m into 504 <latex>$\mu$</latex> m diameter glass tube. During a single orbit the measured particle velocities and paths in steady flow were in good agreement with those calculated for the fluid, predicted by theory to circulate in closed orbits. Over longer periods, however, single blood cells and latex spheres < 20 <latex>$\mu$</latex> m diameter migrated across the streamlines out of the vortex at a rate depending on the Reynolds number whereas spheres and aggregates of red cells > 30 <latex>$\mu$</latex> m diameter remained in the vortex at all Reynolds numbers. Similar behaviour was noted in pulsatile flow when the vortex moved in phase with upstream fluid velocity and particles described spiral orbits of continually changing diameter. With red cell suspensions of 15-45% haematocrit in steady flow, migration of the corpuscles was also observed and resulted in the formation of a particle-free vortex. In pulsatile flow, cells were always present in the vortex, but their concentration which varied periodically was lower than that in the mainstream. The formation of aggregates of latex spheres and human platelets through collisions occurring in orbit, and their migration to the vortex centre was also observed.