Four two-locus genotype combinations showed statistically significant associations with nonallergic asthma in men after Bonferroni correction for multiple comparisons: GPX1 198PL × CAT −21AA (OR = 11.45; 95% CI 2.49–52.66; Padj = 0.001), GSR TT × GCLM −588CT (OR = 11.58; 95% CI 3.07–43.72; Padj = 0.0001), CAT −21AA × CYBA −930GG (OR = 15.64; 95% CI 2.44–100.3; Padj = 0.001), and GCLM −588CT × CYBA −930GG (OR = 6.71; 95% CI 2.5–17.96; Padj < 0.0001). The gene discussed is CAT; the disease is asthma.