In a method and a magnetic resonance system to determine the T1 time of water and the T1 time of fat in a predetermined volume segment of an examination subject, magnetic field gradients are activated to generate multiple gradient echoes. First echoes are acquired at at least two different echo times based on RF pulses with a first flip angle. A first water magnetization and a first fat magnetization are determined for each voxel of the volume segment from the first echoes, according to the Dixon method. Second echoes are acquired at at least two different echo times based on RF pulses with a second flip angle. A second water magnetization and a second fat magnetization are determined for each voxel of the volume segment depending on the second echoes according to the Dixon method. The T1 time of water and the T1 time of fat for each voxel are determined depending on the first water magnetization of the respective voxel, the first fat magnetization of the respective voxel, the first flip angle, the second water magnetization of the respective voxel, the second fat magnetization of the respective voxel, and the second flip angle.