The woman, who remains unnamed, said she put the bodies in the freezer because "she could not bear to part with them" and thought it was wrong to throw them in the bin.
THOUSAND SIGN PETITION AS MOTHER WHO KILLED THREE-YEAR-OLD SON IS JAILED FOR 11 YEARS
Both of the bodies, which had been wrapped in plastic, were found by the father when he was clearing ice out of the kitchen freezer.
One had been there for 18 months.
Police have since said that both babies were born alive; forensic results have showed that one, a boy, had drowned and the other had died by asphyxiation.
READ: DAD WHO DELIBERATLY LEFT SON TO DIE IN HOT CAR MAY FACE EXECUTION
However the woman from Seville, Spain, has claimed that, while she did give birth to one in the bath, both babies were still-born.
She also insisted that she had only hidden the pregnancies from her husband because he would have been furious at having more children.
The woman, who is said to be in her mid-30s, was arrested in November 2012 while she was eight months pregnant.
READ: POLICE DEFEND MURDER CHARGE DECISION FOR DAD WHO LEFT HIS TODDLER IN HOT CAR FOR SEVEN HOURS
She later gave birth to a girl who now lives with the father, along with their two other teenage children.
Her trial begins in Spain this week with the prosecution asking for 40 years in prison for premeditated murder but the defence says the babies died naturally.