The first and the most important stage in the design of Cellular Manufacturing (CM) systems is the Part Family Machine Group Formation (PF/MGF) problem. In this thesis, different approaches to the PF/MG-F problem are discussed. Initially, the design process of CM systems is overviewed. Heuristic techniques developed for the PF/MG-F problem are classified in a general framework. The PF/MG-F problem is defined and some efficiency indices designed to evaluate the PF/MG-F techniques are presented. One of the efficiency indices evaluates the inter-cell flows and inner-cell densities while another one measures the within-cell work-load balances. Another index measures the under-utilization levels of machines. A number of the most promising PF/MG-F techniques are selected for detailed analysis. These selected techniques are evaluated and compared in terms of the efficiency measures by employing randomly generated test problems. Finally, further research areas are addressed.