Classical theories of management relate to the earliest theories of management, that really led to recognition of management as and independent discipline of work and study. These included the ideas of pioneers like Fredrick W. Taylor, Frank Gilbreth. Max Weber, and Henry Fayol. These theories came into being beginning from late nineteenth century and were considered the core of management theory till about 1930's.
Neo-classical theories of management developed during 1920's and later. These can be broadly divides in two groups - theories related to human aspects of management, and quantitative management techniques.
Each of the theories under classical and neo-classical groups have their own values and limitations. But when we come to the common drawbacks of these theories, i can think of only one. All these theories concentrated on some limited aspect of management, and treated is as if it is the sole or most important aspect of management. Also, as would be natural to any developing discipline of management. Thus while people like Taylor concentrated too much on physical aspects of work, people connected with Hawthorne Studies, erroneously believed that they have discovered truths about shop-floor practices of workmen till then totally unknown to others, and concluded that the key to management lies only in promoting appropriate group behavior.