Kad is the implementation by eMule and aMule of the Kademlia peer-to-peer distributed hash table protocol. Although it agrees with the basic behaviour of the protocol, there are some significant differences. This paper presents the specification of both the Kademlia and the Kad routing tables, using the specification language Maude. As far as we know, this is the first such a formal development. The routing tables present a dynamic behavior in the sense that they should be able to send messages to other peers and they should have a notion of time for raising events and detect no answered messages. Our main contribution is the integration of these dynamic aspects in the protocol specification.