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Multifactor dimensionality reduction (MDR) method has been widely applied to detect gene-gene interactions that are well recognized as playing an important role in understanding complex traits, such as disease susceptibility. However, because of an exhaustive analysis of MDR, the current MDR software has some limitations to be extended to the genome-wide association studies (GWAS) with a large number of genetic markers up to ~1 million. To overcome this computational problem, we developed CUDA based genome-wide association MDR (cuGWAM) software using efficient hardware accelerators. Not only cuGWAM has better performance than CPU-based MDR methods (original MDR and parallel MDR) and GPU-based other methods (MDRGPU), but also initial construction cost is also less expensive. Furthermore, cuGWAM provides various performance measures to evaluate MDR classifiers, including tau-b, likelihood ratio, normalized mutual information as well as balanced accuracy. Also, cuGWAM provided three methods for handling missing genotypes: complete, available and missing category. Executable cuGWAM are freely available at http://bibs.snu.ac.kr/cugwam for system with CUDA-enabled GPU devices.