Twins Alfie and Harry McQuillan died after being given more than ten times the recommended dose of morphine at Stafford Hospital.
Parents, Philip and Ami Dean, from Stafford, were taken to Stafford Hospital on October 30th 2010.
Alfie was delivered by caesarian at 5.09am, his brother Harry a minute later.
They were 13 weeks premature.
Soon afterwards they were given morphine to stablise them before being transferred to the University Hospital of North Staffordshire - which was better equipped to look after them.
Alfie was given 600mg, Harry 850mg - the prescribed amount is 50mg.
Their condition deteriorated.
They were transferred to University Hospital of North Staffordshire but died on November 1st.
An inquest today heard how Stafford Hospital wasn't equipped to deal with babies under 32 weeks.
Recording a narrative verdict, the coroner said the twins had died from complcations of extreme prematurity and that the morphine overdose was likely to have played a role in their deaths.
The coroner said their were failings in the care the twins received and today Stafford hospital apologised.
The couple are now expecting another baby. But the pain of losing the twins is still raw.
They say they're still stuggling to come to terms with what happened at Stafford Hospital - as they believe it was two deaths which could so easily have been avoided.