Forecasting is an essential function in the electricity supply industry. Electricity demand forecasting is performed on number of different time-scales depending on the function for which they are required. In the short term (hourly) forecasts of electricity demand are required for the safe and efficient operation of the power system. Medium term forecasts (weekly) are needed for economic planning and long term (yearly) forecasts are required for deciding on system generation and transmission expansion plans. In recent years the electricity supply industry in some countries has undergone significant changes mainly due to a levelling off in the growth of electricity demand and also due to technological advances. There has been a move toward the existence of a number of smaller generating companies and the emergence of a competitors market has resulted. These changes in the structure of the industry have led to new requirements in the area of forecasting, where forecasts are now required on a small time-scale over a longer forecasting horizon, for example, the production of hourly forecasts over a period of a month. The thesis presents a novel approach to the solution of the production of short term forecasts over a relatively long term forecast horizon. The mathematical formulation of the technique is presented and an application procedure is developed. Two applications of the technique are given and the issues involved in the implementation investigated. In addition, the production of weekly electricity demand forecasts using the optimal form of the available weather variables is investigated. The value of using such a variable in cases where it is not a dominant influencing factor in the system is assessed. The application of neural networks to the problem of weekly electricity demand forecasting is examined. Neural networks are also applied to the problem of the production of both aggregate and disaggregate electricity sales forecasts for up to five years in advance. Conclusions regarding the methodologies presented in the thesis are drawn and directions for future works are considered.