It's caused by tiny mites that lay eggs beneath the skin's surface, causing the dogs to scratch and bite themselves, leaving them in pain, irritated and furless.
Now, the 12-week-old pups have been rescued by the RSPCA Millbrook Animal Centre in Surreywhose staff are helping the dogs get back to full health.
They have presented with festive knits to keep them cosy and stop them itching, giving their coats a chance to grow back.
Deputy manager Liz Wood said: "Poor Holly and Ivy have lost a lot of their fur so we're having to keep them snug and warm in special Christmas jumpers.
"These poor little dogs were dumped beside the road like rubbish, it's disgusting.
"They've got a really bad case of mange and are practically bald which means they'd have been even more vulnerable to the cold and rain.
"Thankfully, someone spotted them and asked us for help and we were able to get them into our warm, dry kennels quickly."
The dogs, so desperate for their warm fur to return, have asked staff to help them write letters to Santa Claus (or should we say Santa Paws) to ask for just one thing this Christmas and that is for their coats to re-grow.
The letter reads: "Dear Santa, we have been very good puppies. We were hoping for Christmas we could have our fur back.
"We were dumped by the side of a road covered in mange. So we would love our bald patches to disappear.
"Love Holly and Ivy, aged 12 weeks."
Whilst the siblings recover and wait to see if Father Christmas comes to their aid, they will stay with the RSPCA, but they hope to be adopted in the new year.
In the meantime the centre is asking for Christmas presents for Holly and Ivy.
If you'd like to donate special chews, treats, or toys to keep them or other abandoned fur-babies at the centre amused then please donate here.
It will give all the sad doggos the Christmas they deserve.
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