Durum wheat (Triticum durum desf.) is one of the most important cereal crops used to make pasta, macaroni and other foods. Understanding the complexity of the genotype × environment interaction (GEI) and its impact on determining the most stable genotypes, mega environments and other adaptation goals has been a special concern for the plant breeders. Various methods exist for the stability analysis of grain yields based on different sustainability concepts that can be grouped into parametric, nonparametric and multivariate methods. In this research, 20 genotypes of durum wheat (19 advanced genotypes and Dehdasht commercial variety) were evaluated in five regions during four years (2009-2013). Experiments were carried out in a randomized complete block design with four replications in each environment (year × location). Based on the results of grain yield stability assessment using 13 nonparametric methods in the methods of mean rank, standard deviation and adaptability percentage, genotypes 9, 10 and 12, in the methods of Nassar and Huhn and sum rank of Kang, genotypes 4, 5, 10, 11 and 17 and in the Thennarasu and Fox methods, genotypes 6, 9, 10, 12, 13 and 17 were selected as the most stable genotypes. Finally, based on summarizing the results of all methods genotypes 10 and 12 were selected as the most stable genotypes. According to the previous studies of the authors, it is suggested that in the next researches, in order to better evaluate the stability of genotypes, one of the sustainability methods such as AMMI, spatial regression or mixed models, along with nonparametric methods, must be considered.