Three-month-old baby Chris Kahui died at the Starship hospital last night - almost 14 hours after his twin brother Cru passed away.
The infants had serious head injuries and had been on life support. Police have begun a double-homicide inquiry.
The twins were admitted to the Starship last Tuesday. One baby also had a broken thigh bone.
Child, Youth and Family has removed two older children from the family's Mangere home.
The agency says it had no involvement with the family before the twins were admitted to hospital.
Cru died at 5am yesterday after being taken off life support. Chris died at 6.45pm.
Detective Senior Sergeant John Tims said yesterday that the police were not interviewing any suspects and no charges were pending.
A team of 14 officers had been carrying out inquiries since the babies were admitted to hospital.
Mr Tims said "a number of people" lived in the family home but he did not want to go into detail.
"It's still very early in the piece."
Autopsies on both boys are due to be carried out today.
The babies were born prematurely and spent their first six weeks in the neo-natal intensive care unit at KidzFirst hospital in South Auckland.
Members of the twins' extended family spoke to the media on Saturday night and the father was reported to be at the Starship.
Their maternal grandfather told the Herald on Sunday the family were working through lawyers to have the other children returned.
A CYF spokeswoman said there were no immediate plans to return the children, who were being cared for in a "safe and secure environment" while police investigated.
Lorraine Williams, CYF general manager of operations, said the harming of the twins was a tragedy, "not just for the family but for all of us, knowing that this could and should have been prevented".
The other children in the home had been removed to ensure their safety.
"In every child's life there are family, friends, schools, doctors and nurses. A whole community of people, each of whom has the opportunity to make a difference.
"We each of us need to take personal responsibility for acting to prevent these tragedies."
Children's Commissioner Cindy Kiro said it was too early to say if her office would carry out an inquiry.
She said 80 per cent of children who were killed in New Zealand between 1991 and 2001 were not known to CYF.
"There is a profile to the kinds of babies and children who are killed. They come from environments where family violence is more common, substance abuse is more common, there is a history of mental illness, untreated or treated - in particular post-partum. We forget postnatal depression is quite often a feature, too."
Dr Kiro said people who witnessed injuries on children or had major concerns needed to take action.
"Almost always, somebody knows. Other family members or friends who are visiting witness the behaviour."
New Zealand has the third highest rate of child murder among 27 OECD countries.
Second twin dies of head injuries
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