Yes, wild goats have called Rocky Hill their home and like apparitions they seem to appear at various places on the hill at around sunset each evening.

They can be seen to frolic and gambol over the rocky escarpment and they even enjoy jumping up cheekily onto the corners of the base of the War Memorial.

A photo of the goats cheekily posing on the War Memorial was snapped last week by Eastgrove resident Tash Burleigh, confirming their existence.

Ms Burleigh was walking on the hill with her sister on Thursday night when she was startled by the goats.

“They just ran out of the bush in front of us and we followed them up onto the War Memorial,” she said.

“They looked like they were posing for a moment to take in the view when I took their photo. They are just adorable.”

And they have created a sensation on social media too, after Ms Burleigh posted the pic on the Goulburn Buy Swap and Sell Facebook page.

But not everyone is happy with their presence on the hill.

The Goulburn War Memorial volunteers say the goats are causing too much destruction.

One of the War Memorial volunteers Phillip Fowler pointed out where the goats had been eating the garden outside the Museum.

He claims they have also knocked down large rocks from a rock wall.

“We will have to catch them and re-home them because they are doing too much damage up here,” Mr Fowler said.

“They just turned up one day. We think they have come from over the back of Mt Gray. 

"There are heaps of wild goats over at the back of the dump. 

"Maybe this group came over for a visit and decided to stay?

"They seem well fed.”

Mr Fowler said Council Rangers had been up on the hill to try and catch them, but the goats had given them the slip.

“The rangers asked around neighbouring properties if anyone owned them - but nobody did,” he said.

And while the goats continue to elude the rangers and the War Memorial volunteers - judging from the reaction on social media - most people want them to stay on the hill where they are delighting children and parents alike.

Maybe they can become the city’s next tourist attraction? 

One thing is for sure - they are certainly causing a stir.