This wok investigates the convergence and the performance of Genetic Algorithms: the problems, solutions and proposed measures. It is divided into five topics: a discussion on the mathematical foundations that explains how Genetic Algorithms work: a study of the most important problems associated to their convergence and performance; an analysis of techniques and alternative Genetic Algorithms to achieve better convergence; a study of measures trying to estimate the level of difficulty for the convergence of GA s; and case study. The mathematical foundations are based in conceps of schema and building blocks, developed by Holland (apud Goldberg, 1989a). Although they constitute the fundamental theory about Genetic Algorithms convergence, there has been a lot of questions about the process in which schemata interact during the evolution of GA s (Forrest et al, 1993b). This work presents a discussion on the most important questions that have been raised about the validity of these foundations. Specifically the objections pointed out by Thorton (1995) about the conference of the association between schema and building blocks; the contradiction between schema theorem and Price theorem, mentioned by Altenberg (1994); and the new ideas raised by the variance of fitness concept. The most important problems related to the convergence and performance of GA s are discussed, i.e. the Deception and the Epistasis. Even though Deception can difficult the convergence, the former does not constitute a sufficient factor for the late (Grefenstette, 1993). The Walsh coefficients (Goldberg, 1989b0 and their relation with schema are presented, and also their utilization in deceptive fuctions. Some functions are analised, based on the concepts of Deception and Epistasis: the 6-bits fully- deceptive function by Deb et all (1994): the 3-bits fully- deceptive functions, by Deb et alli (1989); the functions deceptive but easy and non-deceptive but hard of Grefenstette (op. cit.) the F2 and F3 functions of Whitley (1992) as well as the NK functions (apud Harvey, 1993) and the Royal Road functions (Forrest et al, op. cit.). The techniques included the alternative GA s, with special carachteristics. The Messy GA of Goldberg (1989), the Structured GA of Dasgupta (s.d.), the Augmenated GA of Grefenstette (ibidem) and GA s fo Paredis (1996b). The importance of a correct choice of parameters is also discussed. The study of measures classifies those Ga´s into two types: probabilistics and based on landscapes. The considerations of Koza (1994) and Altenberg (op. cit.) are also discussed. It is given special enfasis to the FDC ( Fitness Distance Correlacion) measure, proposed by Jones and Forrest (1995b). The case study consists of the analysis of the behavior of GA by the measure FDC, applied to a set of mathematical functions. The environment used is GENEsYs 1.0, developed by Thomas Bäck (1992) over the Genesis of Grefenstette. The GENEsys 1.0 was adapted and expanded to fullfil the requirements of this work.