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Three adaptive versions of the Ho-Kashyap perceptron training algorithm are derived based on gradient descent strategies. These adaptive Ho-Kashyap (AHK) training rules are comparable in their complexity to the LMS and perceptron training rules and are capable of adaptively forming linear discriminant surfaces that guarantee linear separability and of positioning such surfaces for maximal classification robustness. In particular, a derived version called AHK II is capable of adaptively identifying critical input vectors lying close to class boundaries in linearly separable problems. The authors extend this algorithm as AHK III, which adds the capability of fast convergence to linear discriminant surfaces which are good approximations for nonlinearly separable problems. This is achieved by a simple built-in unsupervised strategy which allows for the adaptive grading and discarding of input vectors causing nonseparability. Performance comparisons with LMS and perceptron training are presented