Polyurethanes (PUs) such as foams or coatings are generally obtained by polyaddition between polyols and toxic polyisocyanates. In the frame of green chemistry principles, which claims, for example, that the reduction of hazardous derivatives and the design of safer chemicals, aza-Michael addition has been recently explored to substitute, for instance, the usual PUs in a safer way. Aza-Michael reaction is based on the addition between a primary or secondary amine (Michael donor) and an activated double bond (Michael acceptor). In this study, polymer network formations from biobased soybean and olive oil derivatives were largely investigated via aza-Michael addition. First, on a reactional model, the impact of the Michael donor structure on the aza-Michael reaction was demonstrated by deep NMR kinetics. Second, the model results were confirmed by monitoring of the aza-Michael polyaddition by multiwave rheology experiments. The effect of several factors, i.e., Michael donors, Michael acceptors, catalysts, and stoichiometry, on the gelation has been largely investigated. Controlling these parameters, the aza-Michael polyaddition was evaluated as a substitute for green and safer thermosets.