The effect of chemical composition on the rheology of a reversible covalent bond containing polyethyleneimine (RCBP) was studied. RCBPs, also known as vitrimers, exhibit thermoplastic‐like processability, but unlike thermoplastic polymers, their behavior is not driven by disentanglement, and all the bonds undergo transformation (almost) simultaneously at constant average crosslink density. Therefore, no lower plateau was observed in a viscosity‐shear rate plot. Transimination, the principal mechanism that imparts flowability, consists of two mechanisms—imine exchange and imine metathesis. Metathesis is only activated by heat, while imine exchange is activated also by stress. Imine metathesis provides low viscosity values at higher crosslink density. A lower viscosity (1092 []Pa0.25emnormals compared to 22,986 []Pa0.25emnormals at 100 Hz) was accomplished by adding 4 wt% triethylenetetramine (TETA). An Arrhenius‐type behavior is shown via relaxation tests with three distinct regions—up to 125°C (only imine exchange), between 125°C and 160°C (imine exchange and imine metathesis) and above 160°C (imine reduction to amine). Imine metathesis seems to promote flow at intermediate temperatures, and at around 150°C, the material behaves as a viscous fluid, otherwise at higher or lower temperatures the dynamic behavior is that of an elastic solid.