The teams experienced vastly contrasting fortunes at the 2023 Rugby World Cup in France with the Springboks winning a record fourth title and the Wallabies failing to reach the knockout stage.
But two-time World Cup-winning coach Erasmus told a press conference at a Johannesburg hotel that he expects "tightly contested" Tests in Brisbane and in Perth seven days later.
"They will present big challenges for us. We have done our homework on the Wallabies, but I anticipate two tightly contested internationals.
"It will be a bit more difficult because some of the (Australian) players are new to us, but (coach) Joe Schmidt certainly is not new to us. We know they will be well organised.
"There are lots of new names in the Wallabies squad, who we have not played against in the last couple of years.
"What is a bit different is that in the past South African clubs were participating in Super Rugby and facing Australian teams regularly.
"I worked under him (Schmidt) when I was at Munster. He is a very hard worker. He is definitely a coach who brings the best out of players."
Erasmus acknowledged that South Africa had won only five of 31 away Tests against Australia in the professional era.
"I am well aware of our poor record in Australia and in the past we have tended to make excuses. We are a team that should not be making excuses," said the coach.
"We are flying tomorrow (Wednesday). We trained yesterday and will train today. We will get there on Thursday and have sessions on Friday and Saturday.
"Then we will try to get into a normal training week routine. We just want a normal Test build-up when we get to Australia."
Top ranked South Africa defeated Wales in London, then won and lost against second ranked Ireland and hammered second-tier Portugal at home this season.
Australia overcame Wales twice and Georgia once in build-up matches at home for the southern hemisphere championship.
