This article aims to discuss the management process of the maintenance function of companies depending on the degree of organization maturity concerning maintenance. Maintenance management makes use of some tools and techniques to improve efficiency and minimize the impacts of unplanned stoppages, such as Reliability Centered Maintenance (RCM), Total Productive Maintenance (TPM) and the Failure Mode and Effects Analysis (FMEA). The identification of the degree of maturity on maintenance, leads us to a better planning of actions to implement the more appropriate management strategy and to propose suitable computerized tools, performance indicators, technical analysis and management tools and techniques, providing a set of potential improvements necessary for the successful evolution of the maintenance process and the resulting progress in the maintenance maturity level. Understanding the aspects which define the degree of maturity of an organization may not be an easy task. In this paper, a study of the maintenance function of some companies was carried out in order to define their maturity levels regarding maintenance. A maturity model is also proposed for the maintenance function through the definition of dimensions and levels. Aspects related to maturity levels have been fairly dealt with in various segments of the knowledge and the use of the proposed models have contributed to the achievement of better results in organizations in general.