Polyethylene-based covalent adaptable networks (PE CANs) are obtained by reactive extrusion in a micro-compounder of a commercial maleic anhydride-grafted polyethylene (PE-g-MA) with two tailor-made α,ω-diamine cross-linkers carrying either imine or 1,2,3-triazolium groups as dissociative covalent dynamic bonds. Depending on the chemical nature of the exchangeable bonds, drastically different properties are demonstrated by FTIR, swelling/extractible, reactive dissolution and rheological experiments. The imine-containing PE CAN yields a high gel fraction but rheology and reactive dissolution experiments demonstrate the lack of dynamicity due to side-reactions promoting the formation of non-dynamic covalent cross-links. Such undesirable reaction occurs already during the processing stage from the premature cleavage of the imine bonds into amines, and further formation of permanent imide cross-links by reaction with pendent maleic anhydrides. Conversely, the 1,2,3-triazolium-containing PE CAN presents a lower gel fraction but exhibits viscoelastic properties typical of dissociative CANs. While this material is easily reprocessable by compression moulding, the evolution of the rheological properties at high temperatures (160–200 °C) points toward the occurrence of side reactions slowing down the relaxation dynamics which we attribute to the chemical rearrangement of the 1,2,3-triazolium cross-links. These two examples illustrate the difficulty of using amine-functionalized dynamic cross-links in the synthesis of PE CANs by reactive extrusion using PE-g-MA.