Transposable elements are one of the major components of genomes. Some copies are fully efficient; i.e., they are able to produce the proteins needed for their own transposition, and they can move and duplicate into the genome. Other copies are mutated. They may have lost their moving ability, their coding capacity, or both, thus becoming pseudogenes slowly eliminated from the genome through deletions and natural selection. Little is known about the dynamics of such mutant elements, particularly concerning their interactions with autonomous copies. To get a better understanding of the transposable elements' evolution after their initial invasion, we have designed a population genetics model of transposable elements dynamics including mutants or nonfunctional sequences. We have particularly focused on the case where these sequences are nonautonomous elements, known to be able to use the transposition machinery produced by the autonomous ones. The results show that such copies generally prevent the system from achieving a stable transposition-selection equilibrium and that nonautonomous elements can invade the system at the expense of autonomous ones. The resulting dynamics are mainly cyclic, which highlights the similarities existing between genomic selfish DNA sequences and host-parasite systems.