Eventual leadership has been identified as a basic building block to solve synchronization or coordination problems in distributed computing systems. However, it is a challenging task to implement the eventual leadership facility, especially in dynamic distributed systems, where the global system structure is unknown to the processes and can vary over time. This paper studies the implementation of a leadership facility in infrastructured mobile networks, where an unbounded set of mobile hosts arbitrarily move in the area covered by fixed mobile support stations. Mobile hosts can crash and suffer from disconnections. We develop an eventual leadership protocol based on a time-free approach. The mobile support stations exchange queries and responses on behalf of mobile hosts. With assumptions on the message exchange flow, a correct mobile host is eventually elected as the unique leader. Since no time property is assumed on the communication channels, the proposed protocol is especially effective and efficient in mobile environments, where time-based properties are difficult to satisfy due to the dynamics of the network.