Dynamic after-cavity interaction (ACI) in megawatt-class gyrotrons is investigated that could lead to lower output mode purity and increased level of internal stray radiation. The self-consistent KIT-IHM multi-mode-code SELFT has been modified to extend the simulation domain into the radius up-taper section of the gyrotron cavity where the probability of ACI exists. Studies on four different gyrotron configurations confirm that undesired interactions in the up-taper region can result in additional parasitic oscillations with relative power in the 1%-range.