During this phase alliances are officially established.  In order to establish an alliance both empires must formally declare the other empire as an ally.  If only one empire makes such a declaration without a corresponding declaration from the other empire, the alliance is not established.  Alliances remain in places until one empire breaks the alliance or until one of the empires is officially eliminated.
 
You can maintain alliances with one or two other empires.  In order to ally with a third empire, you must first break an existing alliance.
 
It is important to note that you can ally with two empires who are not allied with (and who may, in fact, hostile to) one another.