The parents of children named after Adolf Hitler and other Nazi figures have lost a custody battle.

Adolf Hitler Campbell, four, and his three-year-old sister JoyceLynn Aryan Nation, will not be returned to the care of their parents after an appeal was denied.

Honszlynn Hinler Jeannie, 2, will also remain in foster care. The three children were removed from their family home in January 2009.

Their unusual names had drawn media attention when Wal-Mart refused to personalise Adolf’s birthday cake.

Heath and Deborah Campbell, from New Jersey, had claimed that the original decision to take the children away was based on unproven accusations and the names.

But the appeals court ruled that there was evidence of neglect or abuse due to violence in the home.

Social workers found that the Campbell’s "recklessly created a risk of serious injury to their children by failing to protect the children from harm and failing to acknowledge and treat their disabilities".

Mr Campbell, who appeared in court with black boots he claimed were owned by a Nazi soldier, has defended his children’s names. He told reporters he liked the name Adolf.

The court will now go back to family court for further consideration.

The judges also noted that Deborah Campbell had recently passed a letter to a neighbour saying her husband had threatened "to have me killed or kill me himself".

The children's father, Heath Campbell, told the Associated Press last year that he believed they were taken into foster care because of their names.

He also alleged that the authorities had relied on unproven accusations made by a neighbour and his ex-wife.