A system may include electronic devices that communicate wirelessly. When positioned so that a pair of devices overlap or are adjacent to one another, the devices may operate in a linked mode. During linked operations, devices may communicate wirelessly while input gathering and content displaying operations are shared among the devices. One or both of a pair of devices may have sensors. A capacitive sensor or other sensor may be used to measure the relative position between two devices when the two devices overlap each other. Content displaying operations and other linked mode operations may be performed based on the measured relative position between the two devices and other information.