Universities have been pressured by governments to change their way of acting and to be more responsible with the requirements of social development to face the challenges of globalization. To this end, universities must use the principles of Open Science, to allow them to be more transparent regarding the dissemination of scientific results. The purpose of this paper is firstly, to determine the progress made in Open Access policies made by the best-ranked universities regarding ARWU. Secondly, to examine influencing factors that enhance the level of openness in researching, in particular, "transparency", "reputation", "participation", "funding", "foundation" and "size". The main results show that those private and older universities, best-ranked in terms of excellence researching and those that have been gradually adopting Open Government policies concerning the dissemination of information through institutional web pages and social participation, are the most interested with complying the recommendations established by the authorities of the Open Science projects.