The son of a millionaire pharmaceutical mogul has died just days after the gruesome death of his father's girlfriend.

Max Shacknai, the son of Medicis Pharmaceutical Corp chief executive Jonah Shacknai, was said to have fallen down the stairs at the family's San Diego mansion last week.

The six-year-old was taken to hospital but could not be resuscitated.

Mr Shacknai and his ex-wife Dina said in a statement about their son: "His loss is unimaginable. Our beautiful son…lives on in both of our hearts."

Four days earlier, Mr Shacknai's girlfriend Rebecca Nalepa – who was 24 years his junior - was found hanged with her hands and feet bound. Investigators are still looking into whether her death was accidental or caused by suicide, but have said they do not think the two deaths were linked.