Antioxidants prevent oxidative stress and exert positive health effects. However, phytic acid among them decreases micronutrients absorption, representing also antinutrient to human and non-ruminant animals. Fifteen bread wheat (Triticum aestivum L.) and 15 durum wheat (Triticum durum Desf.) genotypes were evaluated across six environments to determine contents of phytic acid (PA), inorganic P (Pi), total yellow pigment, total soluble phenolic compounds, free protein sulfhydryl groups (PSH), and also phytic acid P/Pi (Pp/Pi). The objective of this study was to quantify, for each trait the effects of environment, genotype, and their interaction; and the influence of climatic factors on the Genotype x Environment interaction (GEI) by the use of the factorial regression. GEI (P < 0.001) prevailed as source of variation over genotype (P < 0.001) in determining PA content in bread and durum wheat (44.3% and 34.7% of sum of squares-SS, respectively), PSH content in bread and durum wheat (27% and 28.4% of SS, respectively) and total soluble phenolic compounds content in durum wheat (35.5% of SS). The major contribution to the GEI represented climatic variables during stages of stem elongation for PA and phenolic compounds, and also flowering, fertilization, grain formation and grain filling for PSH. Total yellow pigment and Pi contents in bread and durum wheat were predominantly determined by genotype (P < 0.001). Models of climatic variables proved to be efficient in the explanation of more than 92% of the SS of GEI for PA and antioxidants contents.