Victor S. Albis-Gonz´alezRaj K. MarkandaDepartamento de Matem´aticas y EstadisticaUniversidad Nacional de ColombiaBogot´a, 6, D.E., Colombia1. Introduction. In this paper we discuss the structure of rings offractionsofleftEuclideanringsandleftB´ezout rings. Analogous resultsholdforrightEuclideanringsandrightB´ezoutrings. Forthesakeofcompletenesswe give the basic definitions.We say that a ring