Multilayer deposition of stable colloidal particles during the low Reynolds number flow of aqueous suspensions of latex particles through cylindrical pores in track-etched membranes has been experimentally studied. Though multilayer deposition or the role of deposited particles as additional collectors has been recognized before this work, the reason multilayer deposition of particles occurs in the presence of strong interparticle repulsion and the interactions governing the transition from single layer to multilayer deposition have not been elucidated. Because sufficient repulsion exists between particles in a stable suspension to prevent their aggregation by Brownian flocculation, the deposition of particles on top of previously deposited particles to form multilayers is flow-induced. In this paper, we first show that only a single layer of particles will be deposited on the pore surface if strong repulsion exists between particles. We then demonstrate the transition from single layer to multilayer deposition at a sufficiently high flow rate when the interparticle repulsion is reduced by adding an electrolyte (but not exceeding the critical flocculation concentration). Under these conditions, the hydrodynamic force acting on a flowing particle in the vicinity of a deposited particle can overcome the net interparticle repulsion and multilayers of particles can accumulate within the pores. Approximate calculations of the trajectory of a flowing particle in the vicinity of a stationary particle that qualitatively demonstrate the flow-induced nature of the phenomenon are also presented.