During the operation in a modern power distribution system, some abnormal events may happen, such as over-voltage, faults, under-frequency and overloading, and so on. These abnormal events may cause a power outage in a distribution system or damages on the equipment in a distribution system. Hence these abnormal events should be identified and isolated by protection systems as quickly as possible to make sure we can maintain a stable and reliable distribution system to supply adequate electric power to the largest number of consumers as we can. To sum up, we need stable and reliable protection systems to satisfy this requirement. Chapter 1 of the dissertation is a brief introduction to my research contents. Firstly, the background of a distribution system and the protection systems in a power system will be introduced in the first subchapter. Then there will be a review of existing methods of optimum coordination of overcurrent relays using different optimal techniques. The dissertation outline will be illustrated in the end. Chapter 2 of the dissertation describes a novel method of optimum online adaptive coordination of overcurrent relays using the genetic algorithm. In this chapter, the basic idea of the proposed methods will be explained in the first subchapter. It includes the genetic algorithm concepts and details about how it works as an optimal technique. Then three different types of simulation systems will be used in this part. The first one is a basic distribution system without distributed generations (DGs); the second one is similar to the first one but with load variations; the last simulation system is similar to the first one but with a distributed generation in it. Using three different simulation systems will demonstrate that the coordination of overcurrent relays is influenced by different operating conditions of the distribution system. In Chapter 3, a larger sized distribution system with more distributed generations and loads will be simulated and used for verifying the proposed method in a more realistic environment. In addition, the effects of fault location on the optimum coordination of overcurrent relays will be discussed here. In Chapter 4, the optimal differential evolution (DE) technique will be introduced. Because of the requirement of the online adaptive function, the optimal process needs to be accomplished as soon as possible. Through the comparison between genetic algorithm and differential evolution on the optimum coordination of overcurrent relays, we found that differential evolution is much faster than the genetic algorithm, especially when the size of the distribution system grows. Therefore, the differential evolution optimal technique is more suited than the genetic algorithm to realize online adaptive function. Chapter 5 presents the conclusion of the research work that has been done in this dissertation.