Sally Clark, 38, who has always maintained her innocence, was jailed for life after being found guilty by a jury at Chester Crown Court in November 1999.
She was convicted of smothering 11-week-old Christopher in December 1996 and shaking eight-week-old Harry to death in January 1998, at the home she shared with her husband Stephen in Wilmslow, Cheshire.
Three judges began a fresh review of her convictions on Tuesday.
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If the results had been made known at trial, Sally Clark would not have been convicted of murdering Harry or his dead brother Christopher
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Clare Montgomery QC, Clark's counsel
Clark's counsel, Clare Montgomery QC, told the court that for nearly three years after the death of Harry, his mother, her lawyers and their medical advisers believed that there was not any possible natural explanation of his death.
But she said that at the end of 2000, it emerged that there was clear evidence of an infection that had spread as far as Harry's cerebral spinal fluid.
She submitted that evidence of this infection had been known to the prosecution pathologist, Dr Alan Williams, who had conducted post-mortems tests on both children, since February 1998.
Counsel alleges that "he had kept the results secret from Sally Clark and her advisers".
Failed appeal
The microbiological test results on Harry demonstrated that, in all likelihood, he died suddenly in reaction to the staphylococcus aureus bacteria.
In her written argument to the court, the QC stated: "It is obvious that, if the results had been made known at trial, Sally Clark would not have been convicted of murdering Harry or his dead brother Christopher."
Clark's first appeal bid in 2000 failed when the Court of Appeal ruled that the case against the Clark was "overwhelming".
But her case has now been referred back to the Court of Appeal in London by the Criminal Cases Review Commission, which investigates possible miscarriages of justice.
The hearing is expected to last four days.