The pair, who for legal reasons can only be referred to as Tracey and Keith, deny killing sons Marc and Bradley and nephew Joshua, all aged under two, between 1994 and 1997.
They say the children died as a result of Sudden Infant Death Syndrome, or cot death.
Squalid flat
Anthony Hacking, prosecuting, told the jury that all three children died after being smothered by a pillow or some other form of bedding, and that the couple had worked together to kill them.
Pc Greg Brown, described how, in 1994, he was called to the couple's squalid flat in Brighton, where Marc was found unconscious.
He said the flat had dirty nappies strewn across the floor and bedding smelling of urine.
Pc Brown said: "He (Keith) was agitated and appeared upset. I took Marc from him and placed him on the ground," said Pc Brown. He said he began mouth-to-mouth and then heart massage for five minutes until the ambulance crew took over.
"Keith later looked very calm," the officer added.
Forensic tests
The baby was taken to hospital, where he was found to be alive but he suffered major brain damage from which he never recovered. He died the following year.
Mr Hacking said fresh blood was found on a blanket the baby was lying on in the ambulance, which indicated he had been smothered.
The court heard that the blanket was later destroyed before any forensic tests were carried out to support the claim.
Keith's five-week-old nephew Joshua was the second child to die, in March 1997, Lewes Crown Court heard.
The baby had been left with the couple by Keith's sister because she had to go to court.
While in their care the child was taken to hospital with breathing difficulties. He died four days later.
The cause of death was given as inflammation and swelling of the colon, but the prosecution alleged that the child had also been smothered.
Police investigation
When the couple's six-week-old son Bradley died in similar cirumstances three weeks later, police launched an investigation.
After their arrests, Tracey blamed her husband for all three murders and absolved herself from any part, the court heard.
The prosecution said they would produce evidence that the three children were deliberately smothered.
The couple also deny a charge of cruelty.
The case continues.
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