The voltage stability problem in electric power systems is concerned with the analysis of events and mechanisms that can lead a system into inadmissible operating conditions from the voltage viewpoint. In the worst case, total collapse of the system may result, with disastrous consequences for both electricity utilities and customers. The analysis of this problem has become an important area of research over the past decade due to some instances of voltage collapse that have occurred in electric systems throughout the world. This work addresses the voltage stability problem within the framework of artificial neural networks. Although the field of neural networks was established during the late 1940s, only in the past few years has it experienced rapid development. The neural network approach offers some potential advantages to the solution of problems for which an analytical solution is difficult. Also, efficient and accurate computation may be achieved through neural networks. The first contribution of this work refers to the development of an artificial neural network capable of computing a static voltage stability index, which provides information on the stability of a given operating state in the power system. This analytical tool was implemented as a self-contained computational system which exhibited good accuracy and extremely low processing times when applied to some study cases. Dynamic characteristics of the electrical system in the voltage stability problem are very important. Therefore, in a second stage of the present work, the scope of the research was extended so as to take into account these new aspects. Another neural network-based computational system was developed and implemented with the purpose of providing some information on the behaviour of the electrical system in the immediate future. Examples and case studies are presented throughout the thesis in order to illustrate the most relevant aspects of both artificial neural networks and the computational models developed. A general discussion summarises the main contributions of the present work and topics for further research are outlined.