According to the port's statement, Maersk Skarstind arrived on July 15, whereas the second one, MSC Elma, is expected to arrive on July 20.
Each vessel has the capacity to carry 9,400 TEUs, which is almost the doubled capacity that most containers that visit Australia can handle.
Moreover, both vessels feature a length of 300 meters and a width of 48 meters.
MSC Archimidis, which called at Fremantle late last year for the first time, is 17 meters longer than the ships, Maersk Skarstind and MSC Elma are wider, can carry more containers and have a larger gross tonnage.
In the meantime, Maersk's Maersk Skarstind iys the first twin-island container vessel to arrive in Australia.
The port also stated that in the past week, both vessels were arriving in major Australian container ports, as their last Australian call was the Port of Fremantle.
Chris Leatt-Hayter, Fremantle Ports CEO commented
The Fremantle Inner Harbour can handle ships of this size and draft, the biggest container ships calling at Australian ports, and we expect to welcome even bigger ships in the future.