Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines which are natural extensions of multi-category support vector machines originally proposed by Crammer and Singer. Based on the algorithm stability, we obtain the generalization error bounds for the kernel machines proposed in the paper. Support vector machines are originally designed for binary classification. How tofficient extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines which are natural extensions of multi-category support vector machines by Crammer and Singer. Based on the algorithm stability, we obtain the generalization error bounds for the kernel machines proposed in the paper.