Coronary artery bypass grafting (CABG) plays an important role in the treatment of symptomatic coronary artery disease. During the fifty years since the first operation, a great amount of clinical observations confirm that the internal mammary artery (IMA) can be used for the bypass grafting by the most favorable outcome. IMA's histological structure and physiological properties make it resistant to atherosclerosis. In our article, we remember the first CABG operation in Hungary using IMA graft and we also confirm the favorable properties of IMA by the results of the 35-year follow-up, with the longest reported coronary angiography in the literature after IMA grafting. On the basis of this case, we can speculate that the prostacyclin secretion of the mammary graft can prevent the run-off tract of the left anterior descending (LAD) artery from the atherosclerotic progression. Large-scale study is warranted to compare the long-term prognosis of the run-off tract after grafting versus stenting of the LAD. Orv Hetil. 2020; 161(9): 354-358.