Nuclear disks and rings are frequent galaxy substructures, for a wide range of morphological types [from S0 to Sc, see e.g., 1, 2]. We have investigated the possible minor-merger origin of inner disks and rings in spiral galaxies through collisionless N-body simulations. The models confirm that minor mergers can drive the formation of thin, kinematically-cold structures in the center of galaxies out of satellite material, without requiring the previous formation of a bar. Satellite core particles tend to be deposited in circular orbits in the central potential, due to the strong circularization experienced by the satellite orbit through dynamical friction. The material of the satellite core reaches the center if it is dense or massive, building a thin inner disk. Instead it is fully disrupted before reaching the center in the case of low-mass satellites, creating an inner ring.