A320 Captain reported the loss of both ELACs in cruise. The flight crew requested priority handling and continued to the destination airport in Alternate Law. A precautionary landing was made.

Narrative

In cruise flight at FL340 we got an ECAM; ELAC 2 Pitch Fault. After performing ECAM actions and referencing the communications (COM); it was a crew awareness item. Approximately 30 minutes later at the top of descent on the ZZZZZ arrival we received an ECAM of ELAC 1 Pitch Fault; autopilot off; Alternate law with all Protection lost. After performing ECAM and referencing the COM we decided that we were stuck in Alternate Law and the COM referenced us to perform the Alternate Law procedure. After going over that we decided that continuing on the arrival and landing in ZZZ was our best option. It was also a perfect weather day in ZZZ. We landed with Flaps 3 and also Vref plus 10 per the procedure. We requested priority handling knowing we would eventually land. Briefed the Flight Attendants that we expected a normal landing but they would see the crash fire rescue (CFR) trucks and if anything changed we would let them know. Also made a PA explaining what happened and also that they would see the CFR trucks and this was a precautionary situation but we expected a normal landing. We then proceeded to ZZZ and made a successful; normal landing in direct law. Continued to the gate with no further incidence after talking to CFR and releasing them.