Monolayers of intermediate-length alkane molecules such as tetracosane (n-C24H50 or C24) serve as prototypes for studying the interfacial dynamics of more complex polymers, including bilayer lipid membranes. Using high-resolution quasielastic neutron scattering (QNS) and exfoliated graphite substrates, we have investigated the relatively slow diffusive motion in C24 monolayers on an energy/time scale of similar to1-36 teV (similar to0.1-4 ns). Upon heating, we first observe QNS in the crystalline phase at similar to160 K. From the crystalline-to-smectic phase transition at similar to215 K to a temperature of similar to230 K, we observe the QNS energy width to be dispersionless, consistent with molecular dynamics simulations showing rotational motion of the molecules about their long axis. At 260 K, the QNS energy width begins to increase with wave vector transfer, suggesting onset of nonuniaxial rotational motion and bounded translational motion. We continue to observe QNS up to the monolayer melting temperature at similar to340 K where our simulations indicate that the only motion slow enough to be visible within our energy window results from the creation of gauche defects in the molecules.