The T1 relaxation of triglyceride molecules is of interest for fat-water separation and fat quantification. A better understanding of the T1 of fat could benefit modeling techniques for applications in MR-oximetry and fatty liver disease. In this work, the T1 relaxation and its dependence on fat content was evaluated for five spectral peaks present in triglyceride molecules, over a range of fat fractions in a homogeneous fat-water mixture. The T1 of water in mixture was also studied. A model is proposed to describe the two-pool relaxation in a fat-water mixture as a function of the fraction of each pool.