A 12-year-old refugee on Nauru has not eaten for nearly two weeks while a Manus Island refugee is also refusing food and water.
The ABC reported medical staff on Nauru saying the 12-year-old boy was on a hunger strike.
He had been sedated and given fluids to keep him alive, they said.
The Iranian-born refugee has been held on the island, along with his family, for five years.
Refugee advocacy organisation Doctors for Refugees has been monitoring the boy's health.
"Doctors have had concerns about this young child for a very long time," Doctors for Refugees president Dr Barri Phatarfod told the ABC.
"He's got quite a difficult family situation, and it's been almost two weeks now that he's refused food and fluid.
"He's severely depressed. I don't really want to say much more about his personal medical condition but it's pretty obvious that when you've got a child that refuses to eat or drink for up to two weeks they are profoundly depressed."
The Iranian boy is one of several children on the island who advocates say are suffering from resignation syndrome.
Children with the syndrome become unresponsive and stop talking, eating, drinking, and going to the toilet
It is not known whether the Iranian boy will be flown to Australia for treatment.
Lawyers from Maurice Blackburn have won three recent cases to bring children to Australia - a baby, a toddler, and a young girl.
Another refugee, on Manus Island, was also refusing food and water but was mentally ill and not on a hunger strike, according to another refugee.
The man had locked himself in his room for days at the East Lorengau Transit Centre until healthcare providers intervened on Tuesday.
The Kurdish refugee and journalist, Behrouz Boochani, said the man was taken to the island's hospital and rehydrated overnight with an intravenous drip.
He was returned to the centre on Wednesday and given antibiotics on Thursday for pain in his kidneys, Mr Boochani said.
The man was severely depressed and not eating yesterday but psychiatric help was not available on the island, the journalist said.
Psychiatry professor at Melbourne University Louise Newman said the man could be in a state of withdrawal due to profound depression.
Convener of the advocacy group Doctors For Justice, Prof Newman said other refugees had been found in a similar state in offshore detention, "but political hunger striking is a very different issue".
About 600 refugees are housed in three centres on the Papua New Guinea Island where they have been exiled since 2013.
Many of the men have developed mental health issues during their indefinite incarceration, which are thought to have led to several deaths amoung the 12 that have occurred in Australian offshore detention.
Another refugee suffering from severe mental illness is currently in Port Moresby.
Accused of setting fire to one of the centres, the refugee was sent to the capital for an operation after he damaged his wrist punching a window.
Kurdish refugee in Port Moresby Benham Satah said the man received surgery earlier this month from a visiting Indian surgeon.
He appeared to be suffering from delusions, however, and had left the hospital three times during his recovery, most recently on Thursday night, Mr Satah said.
At one stage the man had tried to unfasten the stitches in his wrist until friends intervened.
"We have seen him with no mental illness so we know what this long, illegal detention did to his mind," Mr Satah said.
The man was now in Port Moresby's Granville Motel where other refugees stayed while receiving medical treatment.
"The surgeon was optimistic about it," said Mr Satah who interpreted for some of the patients, "otherwise he's lost his right hand."
Most of the refugees were suffering from mental illness on Manus Island, he said, but the man accused of arson was "very, very mentally sick, maybe more than anybody else".
"I truly hope something is done for him before it's too late."
Being stateless and displaced in a "threatening and hostile" environment was contributing to an increase in psychological distress amoung the men, Prof Newman said.
"The terrible tragedy is that in many ways this sort of deterioration is quite predictable," she said.
"What it should lead us to do is have a radical rethink of the damage that's being done, the need to inflict this on people, and about who is actually going to treat and care for the damage that the system produces."
- RNZ / ABC