In recent years, Airyprime pulses have attracted much attention in the field of nonlinear optics due to their diffraction-free, self-accelerating, and self-healing properties, as well as their unique oscillating tail structure. However, Airyprime pulses are affected by higher-order dispersion and Raman effect in the relaxation nonlinear medium, and their propagation properties have not been thoroughly studied. To this end, the propagation properties of Airyprime pulses in relaxing nonlinear media are systematically investigated in this article ...