A series of acylamide and amine oxide derivatives of polyethylenimine, both hyperbranched (HPEI) and linear (LPEI), has been synthesized, and their performance as kinetic hydrate inhibitors (KHIs) with a structure II (SII)-forming natural gas mixture has been investigated in high-pressure steel rocking cell experiments. This is the first time that the ICHI performance of linear and hyperbranched polymers with the same functional groups has been compared. The importance of quality control in KHI synthesis is also highlighted. In general, the amine oxides showed better performance than the acylamides when comparing the structurally optimized and best polymers from each class. The amine oxide polymers with best KHI performance were the low-molecular-weight butylated HPEI amine oxides. The performance was similar to those of oligomeric amine oxides reported previously with molecular weights as low as 660 g/mol. This contrasts with other KHI polymer classes, where molecular weights below 1000-1500 g/mol generally give poor KHI efficacy. In previous work, the linear LPEI amine oxides were shown to be excellent tetrahydrofuran SII hydrate crystal growth inhibitors, superior to hyperbranched HPEI derivatives. However, the LPEI amine oxides were poorer gas hydrate KHIs than the HPEI derivatives, suggesting that other mechanisms besides crystal growth inhibition, such as nucleation inhibition, may be the dominant mechanism for this class of KHI. Acyl amide polymers with n-propyl pendant groups performed only a little better than equivalent polymers with isopropyl groups and far better than polymers with ethyl groups. This trend is in line with a lowering of the cloud points of the polymer as the hydrophobicity increases. Acylamides based on linear LPEI gave better performance than those based on hyperbranched HPEI. The reasons for this are discussed. Linear amine oxides based on LPEI gave lower performance than hyperbranched or oligomeric amine oxides, which may be related to the availability of primary amine groups in HPEI or oligomeric ethyleneamines.