A jury was discharged from Winchester Crown Court
Angela Cannings, 38, is alleged to have murdered seven-week-old Jason Cannings in June 1991, and four-month-old, Matthew Cannings in November 1999 as they slept in their cots.
Paul Dunkels QC, prosecuting, told the jury at Winchester Crown Court that Mrs Cannings was the only other person in the house when the deaths occurred.
The trial of Mrs Cannings was halted on Wednesday morning and the jury discharged by Mrs Justice Hallett.
Fresh jury
The reasons for the discharge of the jury cannot be revealed for legal reasons.
A new jury panel was sworn in and the case opened to a fresh jury.
Mr Dunkels told the court that as well as the deaths of Jason and Matthew, Cannings first child, Gemma, had also died in 1989 and another child in her care had suffered an "acute life-threatening event".
Life-threatening
He told the jury: "For a mother to attack a child in this way is against nature and instinct but the prosecution say that the evidence will demonstrate this is what Angela Cannings had done to her two babies."
Mr Dunkels said that Mrs Cannings was not charged with any offence regarding the death of Gemma or the other incident involving another child, but he told the jury "the fact of Gemma's death is the backdrop in which you will have to consider what happened to Jason and Matthew."
Mr Dunkels told the court that Jason suffered a life-threatening event nine days before he died.
Health visitor Gloria Peacock arrived to see Mrs Cannings and Jason when the incident happened and she had managed to revive the baby who made a full recovery.
'On own'
But Mr Dunkels said that it was the prosecution's case that Mrs Cannings had "deliberately obstructed" the breathing of her baby as it lay in its cot in a flat in a village of Winterbourne Gunner, Wiltshire, in June 1991.
He told the court that on every occasion of either the death of her babies or a life-threatening incident, Mrs Cannings had been on her own with her children.
Mrs Cannings, who is represented by Michael Mansfield QC, denies murdering Jason and Matthew.
She also denies harming any of the children.
The trial was adjourned until Thursday, when the jury is to visit the houses in which Mrs Cannings lived at the time of the alleged murders.