The embodiments herein relate to a method in a mobility management node (108) for handling overload in a communications network (100). When overload in the communications network (100) has been detected, the mobility management node (108) receives information indicating at least one blocked IP address to which access should be blocked. The mobility management node (108) receives a communication request message from a UE (101) via a RAN node (105). The communication request message is a request for communication by the UE (101). The mobility management node (108) determines that the UE's (101) request for communication should be rejected when the UE (101) is associated with a blocked IP address.