We report the multi-component optical azimuthons of four-wave mixing (FWM) composed of several modulated vortex beams, the so-called azimuthons, in V-type three-level and two-level atomic systems. We analyze the formation mechanisms of the FWM azimuthons theoretically and experimentally. In addition, we illustrate the interactions between the co-propagating azimuthon components. Finally, we also compare the stabilities of azimuthons in V-type three-level and two-level atomic systems.