The system of vortices created by the hub and tip vortices of rotors and propellers is composed of two subsystems of helical vortices that have different radii and pitches. A similar system of external and internal vortices is created by some blade devices proposed to destabilize the tip vortices of helicopters. The steady solution of these systems of vortices was recently described. However, their stability was not studied. The stability of a system of multiple helical vortices was studied in this work using a complex-step technique to linearize the Biot-Savart law and the vorticity transport equations. It was noted that the hub and tip vortices do not interact and their linear stability can be treated separately, if the velocity field induced by one system is considered in the stability of the other. For a ratio of radius of 0.8, strong interaction between the vortices was observed, with an out-of-phase mechanism appearing as one of the main phenomena.