We discuss the ideal glass transition for two types of potential model of attractive colloidal systems, i.e. the square-well system and the Yukawa hard-sphere fluid. We use the framework of the ideal mode-coupling theory and we mostly focus our attention on the nature of the singularities predicted by the theory. We also study the phenomena that arise by varying the range of the attraction, since this parameter has been identified as one of the key parameters in colloidal systems.