Abstract: In this paper, the implicit enumeration methods for mathematical programming are effectively classified: well-implied and ill-imp lied enumerations. Essential difference between the two kinds of implicit enumeration methods is investigated. The judgment on well-implied enumeration method is given. According to probabilistic convergence of incomplete enumeration, the concept of near-implicit enumeration is proposed. Several typical well-implied enumeration methods and near-implicit enumeration methods are illustrated. In the end, the trend of developing well-implied and near-implicit enumerations is concluded.