Final answer:
The cilia on the oviduct wall are responsible for the movement of an egg or fertilized egg in the oviduct.
Step-by-step explanation:
The structure in the oviduct that an egg or fertilized egg relies on for movement is the cilia on the oviduct wall. The cilia, which are hair-like projections, beat in coordinated motions to create a current that moves the egg or embryo towards the uterus. Additionally, the smooth muscle in the walls of the oviduct contracts in the same direction as the cilia, aiding in the movement of the egg or embryo.