The sustainability of the competitive edge of a company can be analyzed by integrative dynamic models, taking into consideration structural aspects of the industrial sector and the company`s resources and its competence. However, when disturbances in the business environment are of substantial magnitude, such models may not be enough to explain what is happening and what strategy the company must pursue to ensure its competitive advantage. The business environment in the Brazilian petroleum sector has been undergoing disturbances of the form proclaimed by Schumpeter (1934, 2000), that is to say, in a context in which companies can only imperfectly predict alterations. In this context, that which was valid and adapted, up to now, to provide advantageous competitive results for a company, can no longer be so, bringing tragic results for its performance. Since the strategies are devised by drafting out future situations, and since such predictions have a very limited validity in this type of environment, applicability becomes compromised. The question then arises: what factors can lead a firm to sustainability of competitive edge in a context of great changes? Within such a situation, the secret of sustainability might not be merely linked to a company`s competence or to strategic maneuvering, but could be mainly connected with the indirect influence of its less-than- perfect adaptation to the business environment and, as a consequence, with its perception of the need to change and to learn, and with its organizational flexibility.In adopting a systemic approach to the company, centered on strategic conversation, which emphasizes the need for dialogue and accept ance of thinking that is dissident to predominant ideas, a study framework was proposed inspired by the ideas of Argyris (1991), Brown & Eisenhardt (1998), De Geus (1997), Senge (1994) and Van der Heijden (1998), which points out the following critical factors for sustainability of competitive edge in an environment in transition: a sensitive concern for the business environment; a capacity for learning; and organizational flexibility. Using the case study method, applied to the E&P segment of Petrobras, one sought to identify critical factors for sustainability of the competitive edge of the company, with due consideration of its continually-changing business environment. From an analysis of the standard of replies obtained in the survey, and also from observing the dynamics of the company during the survey period, it was possible to conclude that the factors emphasized in the study framework are present in the company. However, some of those factors are still latent, very much due to fact that the organizational transition recently undergone by Petrobras is not yet consolidated. The research survey enabled identification of one other factor critical to the success of the company in the post-transition phase: its capacity for accepting dissident thinking and being able to extract from it what is not perceived by the dominant profile, especially weak environmental signs. Indeed, within the context of consolidating the organizational transformation recently implemented at Petrobras, one can see that space still exists for a greater acceptance of dissident thinking.