The use of a secondary device alongside a first screen, such as a television, is referred to as second screening and is generally considered as a common and widespread behavior. With the advent of smart first screens (smart TVs, set-top boxes, streaming sticks, etc.), this type of activity gained a new perspective in the form of connected second screen applications such as YouTube, Netflix, or Amazon Prime Video which enable functionalities such as the display of additional information or remote control aspects on the second screen. The design of these distributed applications is difficult because the user's attention cannot be focused on both parts at the same time, which is why this paper presents two eye-tracking studies investigating this problem. The studies examined on the one hand the general viewing behavior with second screen applications and on the other hand the targeted directing of attention to the first and second screens. From these results, recommendations for the design of second screen applications are derived and presented, with the aim that the two application parts complement each other rather than competing for the user's attention.