Molecular reorientation in the two amorphous phases of triphenyl phosphite, namely the supercooled liquid (phase aI) and the newly discovered second amorphous phase (phase aII), was investigated by dielectric relaxation and by two-dimensional (2D) nuclear magnetic resonance spectroscopy (NMR) in the time and frequency domain. Whereas phase aI exhibits the relaxational features typical of supercooled liquids, the molecular motion in phase all is characterized by an extremely broad dielectric loss and by a pronounced nonexponential reorientational correlation function. Using a Gaussian distribution of correlation times, both dielectric and NMR data reveal consistently correlation times on the order of seconds. The quantitative analysis of the 2D spectra favors the interpretation that molecular motion in phase all leads to an isotropic distribution of molecular orientation on the surface of a sphere. In addition, we find a secondary relaxation process that shows basically the same features in both phases. We conclude that the newly discovered phase is a second liquid phase with a very unusual reorientational correlation function. However, a nematic liquid crystal cannot completely be ruled out.