The rational selection of catalysts and process parameters for co-processing biomass- and waste-derived bio-crudes with petroleum streams requires detailed reaction networks and kinetics of the conversion of heteroatom-containing compounds existed in both kinds of feedstocks. We provide the kinetics and reaction networks for the hydrotreating of N,N-diethyldodecanamide and N-methyldodecanamide, model compounds of major components in bio-crudes from hydrothermal liquefaction of wet waste. Their conversion undergoes via two pathways over sulfided NiMo/Al2O3 catalyst: deoxygenation followed by denitrogenation of the amine intermediate (DO pathway), and denitrogenation followed by deoxygenation of the alkanol intermediate (DN pathway)—with the DO pathway dominant over the DN pathway. H2S inhibits the deoxygenation step and promotes the denitrogenation step in the DO pathway. The amine intermediate inhibits the amide conversion, with weaker effects on the conversion of secondary amide than on the tertiary amide. The kinetics of hydrotreating of several model compounds representing the main species during co-processing indicate that the removal of nitrogenous species, which are in large quantities and of varying structures, remains the main challenge (compared with S- and O-removal) for co-processing.