Most mineral and coal processing plants are forced to size their particulate streams in order to maximize the efficiency of their unit operations. Classifiers are generally considered to be more practical than screens for fine sizing, but the separation efficiency decreases dramatically for particles smaller than approximately 150 μm. In addition, classifiers commonly suffer from bypass, which occurs when a portion of the ultrafine particles (slimes) are misplaced by hydraulic carryover into the oversize product. The unwanted misplacement can have a large adverse impact on downstream separation processes. One method of reducing bypass is to inject water into the cyclone apex. Unfortunately, existing water injection systems tend to substantially increase the particle cut size, which makes it unacceptable for ultrafine sizing applications. A new apex washing technology was developed to reduce the bypass of ultrafine material to the hydrocyclone underflow while maintaining particle size cuts in the 25-50 m size range. Another method of reducing bypass is to retreat the cyclone underflow using multiple stages of classifiers. However, natural variations in the physical properties of the feed make it difficult to calculate the exact improvement offered by multistage classification in experimental studies. Therefore, several mathematical equations for multistage classification circuits were evaluated using mathematical tools to calculate the expected impact of multistage hydrocyclone circuits on overall cut size, separation efficiency and bypass. These studies suggest that a two-stage circuit which retreats primary underflow and recycles secondary overflow offers the best balance between reducing bypass and maintaining a small cut size and high efficiency. / Master of Science