The father, who was not identified, left the children aged 1 to 17 at Creighton University Medical Center's emergency room.
The law, which went into effect in July, allows caregivers to abandon children at any state-licensed hospital without fear of prosecution. It was initially intended to protect infants - like similar laws in other states - but was amended to include children and teenagers.
At least four children between the ages of 11 and 15 have been abandoned by parents since the law took effect.
The nine youngsters surrendered Wednesday are OK, said Kathie Osterman, a spokeswoman for the Nebraska Department of Health and Human Services. She didn't know how many were boys or girls, or why their father left them.
More information will be available at a late morning news conference, Osterman said.
Nebraska was the last state in the nation to adopt a safe-haven law. Under previous law, a parent who abandoned a baby could have been charged with child neglect or abandonment, both misdemeanors, or child abuse, a felony.
State Sen. Arnie Stuthman said he introduced the bill intending to protect infants. In a compromise with senators worried about arbitrary age limits, the measure was expanded to include the word "child."
The law doesn't further define child, and some have interpreted that to mean anyone in Nebraska under the age of 19. Others have taken the common law meaning of child - those under age 14.
Abandoning teenagers was not the original intent of the law, Stuthman said Thursday.
"People are leaving them off just because they can't control them," he said. "They're probably in no real danger, so it's an easy way out for the caretaker."