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Rex Features
The singer, who gave birth to the babies in October, admitted that she and husband Michael Lockwood had taken time to get used to Finley and Harper.
"When we brought the babies home it was a complete and utter shock," she told Hello!.
"Everything is so freaky. Are they breathing? Are they okay? They're so fragile. That freaks me out. Michael was freaked out about dropping them."
Presley already has two children - Riley, 19, and Ben, 16 - from a previous marriage, and claims that the new additions to the family have already developed their own personalities.
"Finley is a little clone of me and Harper is a little clone of Michael, looks and personality wise.
"Little Harper, for 'harp', is this little sweet, calm, dainty baby. And Finley, which is Scottish for 'fair warrior', is also an angel but a bit more rugged. She is ferocious, funny and full of p*ss and vinegar, as they say."
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