A Melbourne study has found more than a third of parents of babies born very prematurely suffer depression or anxiety.

Mothers and fathers of very premature babies struggle with depression and anxiety at a 'concerning' rate, an Australian study has found.

Research conducted by the Murdoch Children's Research Institute showed more than a third of parents of infants born before 30 weeks gestation had depression or anxiety.

Led by Dr Carmen Pace, the researchers followed 113 mothers and 101 fathers of very pre-term babies born at Melbourne's Royal Women's Hospital.

Parents' symptoms of depression and anxiety were documented every two weeks until the infants' expected birth date, and again at six months post-birth.

"While the rates of depression and anxiety declined with time, they remained well above expected levels throughout the newborn period at six months, never dropping below 20 per cent," said Dr Pace.

The study, published in journal JAMA Pediatrics, found shortly after birth 40 per cent of mothers suffered mental health issues compared to six per cent of mothers of full term babies.

For the fathers, 36 per cent reported anxiety or depression compared with five per cent of fathers of full term babies.

At six months after birth of a pre-term baby, the rate of depression and anxiety was 14 per cent for the mothers and 19 per cent for the fathers.

Kirsten and Radford White are parents to twins Rupert and Maisie, who were born at 29 weeks and six days.

They described their experience as an emotional rollercoaster.

"No one plans for a premature baby. And all the plans you had made are now thrown out the window with the premature birth. The reality of NICU admission created on overwhelming sense of helplessness for both Kirsten and myself," Mr White said.

Terri Smith, CEO of the Perinatal Anxiety and Depression Australia (PANDA) helpline, says its important that these vulnerable parents can share their feelings of hopelessness and that they know there is help available.

"It's an extraordinary period of transition to being a parent and starting it out with a whole lot of difficulties is likely to make it a much more difficult time to progress their emotional wellbeing."

"If a mum and dad can leave the hospital knowing that it's really important that they look after their own health and seek help early, because seeking help is really the best way to get better."

The findings also demonstrate that the community needs to be conscious of a fathers' wellbeing too.

"Most dad's remain involved in the day-to-day care of their infants while they are in hospital, and often juggle this with returning to work," Dr Pace said.

* Readers seeking support and information on post-natal depression can phone the free PANDA national helpline on 1300 726 306.