Software maintainability is one of the most important aspects when evaluating the quality of a software product. It is defined as the ease with which the existing software can be modified. In the literature, several researchers have proposed a large number of models to measure and predict maintainability throughout different phases of the Software Development Life Cycle. However, only a few attempts have been made for conducting a comparative study of the existent proposed prediction models. In this paper, we present a detailed classification and conduct a comparative analysis of Object-Oriented software maintainability prediction models. Furthermore, we considered the aforementioned proposed models from three perspectives, which are architecture, design and code levels. To the best of our knowledge, such an analysis that comprises the three levels has not been conducted in previous research. Moreover, this study hints at certain fundamental basics concerning the way of how measure the maintainability knowing that at each level the maintainability will be measured differently. In addition, we will focus on the strengths and weaknesses of these models. Consequently, the comparative study yields that several statistical and machine learning techniques have been employed for software maintainability prediction at code level during the last decade, and each technique possesses its specific characteristic to develop an accurate prediction model. At the design level, the majority of the prediction models measured maintainability according to the characteristics of the quality models. Whereas at the architectural level, the techniques adopted are still limited and only a few of studies have been conducted in this regard.