  We study the time needed for deterministic leader election in the ${\cal
LOCAL}$ model, where in every round a node can exchange any messages with its
neighbors and perform any local computations. The topology of the network is
unknown and nodes are unlabeled, but ports at each node have arbitrary fixed
labelings which, together with the topology of the network, can create
asymmetries to be exploited in leader election. We consider two versions of the
leader election problem: strong LE in which exactly one leader has to be
elected, if this is possible, while all nodes must terminate declaring that
leader election is impossible otherwise, and weak LE, which differs from strong
LE in that no requirement on the behavior of nodes is imposed, if leader
election is impossible. We show that the time of leader election depends on
three parameters of the network: its diameter $D$, its size $n$, and its level
of symmetry $\lambda$, which, when leader election is feasible, is the smallest
depth at which some node has a unique view of the network. It also depends on
the knowledge by the nodes, or lack of it, of parameters $D$ and $n$.
