It was found that satellites of nearby galaxies can form flattened co-rotating structures called disks of satellites or planes of satellites. Their existence is not expected by the current galaxy formation simulations in the standard dark matter-based cosmology. On the contrary, modified gravity offers a promising alternative: the objects in the disks of satellites are tidal dwarf galaxies, that is, small galaxies that form from tidal tails of interacting galaxies. After introducing the topic, we review here our work on simulating the formation of the disks of satellites of the Milky Way and Andromeda galaxies. The initial conditions of the simulation were tuned to reproduce the observed positions, velocities and disk orientations of the galaxies. The simulation showed that the galaxies had a close flyby 6.8 Gyr ago. One of the tidal tails produced by the Milky Way was captured by Andromeda. It formed a cloud of particles resembling the disk of satellites at Andromeda by its size, orientation, rotation and mass. A hint of a disk of satellites was formed at the Milky Way too. In addition, the encounter induced a warp in the disk of the simulated Milky Way that resembles the real warp by its magnitude and orientation. We present here, for the first time, the proper motions of the members of the disk of satellites of Andromeda predicted by our simulation. Finally, we point out some of the remaining open questions which this hypothesis, for the formation of disks of satellites, brings up.