Nanocrystal surfaces are commonly populated by organic ligands, which play a determining role in the optical, electronic, thermal, and catalytic properties of the individual nanocrystals and their assemblies. Understanding the bonding of ligands to nanocrystal surfaces and their dynamics is therefore important for the optimization of nanocrystals for different applications. In this study, we use temperature-dependent, quasi-elastic neutron scattering (QENS) to investigate the dynamics of different surface bound alkanethiols in lead sulfide nanocrystal solids. We select alkanethiols with mono- and dithiol terminations, as well as different backbone types and lengths. QENS spectra are collected both on a time-of-flight spectrometer and on a backscattering spectrometer, allowing us to investigate ligand dynamics in a time range from a few picoseconds to nanoseconds. Through model-based analysis of the QENS data, we find that ligands can either (1) precess around a central axis, while simultaneously rotating around their own molecular axis, or (2) only undergo uniaxial rotation with no precession. We establish the percentage of ligands undergoing each type of motion, the average relaxation times, and activation energies for these motions. We determine, for example, that dithiols which link facets of neighboring nanocrystals only exhibit uniaxial rotation and that longer ligands have higher activation energies and show smaller opening angles of precession due to stronger ligand-ligand interactions. Generally, this work provides insight into the arrangement and dynamics of ligands in nanocrystal solids, which is key to understanding their mechanical and thermal properties, and, more generally, highlights the potential of QENS for studying ligand behavior.