Support vector machines (SVMs) are widely used for solving classification and regression problems. Recently, various nonparallel hyperplanes classification algorithms (NHCAs) have been proposed, which are comparable in terms of classification accuracy when compared with SVM but are computationally more efficient. All these NHCAs are originally proposed for binary classification problems. Since, most of the real world classification problems deal with multiple classes, these algorithms are extended in multi-category scenario. In this paper, we present a comparative study of four NHCAs i.e. Twin SVM (TWSVM), Generalized eigenvalue proximal SVM (GEPSVM), Regularized GEPSVM (RegGEPSVM) and Improved GEPSVM (IGEPSVM)for multi-category classification. The multi-category classification algorithms for NHCA classifiers are implemented using OneAgainst-All (OAA), binary tree-based (BT) and ternary decision structure (TDS) approaches and the experiments are performed on benchmark UCI datasets. The experimental results show that TDS-TWSVM outperforms other methods in terms of classification accuracy and BT-RegGEPSVM takes the minimum time for building the classifier