A leader election algorithm is stable if it ensures that once a process is elected as the leader, it remains the leader as long as it continues to behave well, regardless of the behavior of other processes and links. We present three new leader election algorithms that exhibit stronger stability properties than currently known. Our algorithms are for systems with reliable links. The first two algorithms assume the existence of an eventual hub, i.e., a correct process whose incoming and outgoing links are eventually timely. The third algorithm is the first known stable algorithm that does not assume the existence of a hub: it requires only the existence of an eventual source, i.e., a correct process whose outgoing links are eventually timely. Our stable leader election algorithms are the first ones where the stabilization time does not depend on the rate at which processes send messages.