Social and environmental responsibility of apparel sector has been drawing rising attention of policymakers and researchers in recent years. One possible solution to curb the detrimental effects caused by the clothing industry is to invoke more responsible demand of its heavy users, such as young clothing customers. This study aims to examine a model of the determinants of environmentally and socially responsible clothing consumption of young adult customers in a developing economy. The study has been performed on a convenience sample of 439 respondents in Serbia, by means of structured online survey. Exploratory factor analysis (EFA), followed by two-step structural equation modeling procedure (SEM)—implying an examination of a measurement model, followed by testing of structural relationships—has been performed within data analysis. Results of the study indicate green consumption values as the most influential determinant of responsible apparel consumption, followed by conscious consumption and receptivity to green communication. Findings of the study contribute to the body of knowledge on responsible consumption and provide directions for practitioners and policymakers. Study limitations are noted and future research directions are provided.