A High Court judge is analysing legal issues relating to a dispute between Madonna and her ex-husband Guy Ritchie over the future of their 15-year-old son Rocco.
Mr Justice MacDonald is considering the case at a private hearing in the Family Division of the High Court in London.
The judge has already said it is his "fervent hope" that the singer and film-maker can have discussions and reach an "amicable resolution".
He said the fact that the hearing was taking place could be reported but said no detail could be publicised.
Mr Justice MacDonald has already considered a number of legal issues at a hearing last week.
Similar hearings have taken place in New York following the launch of family court litigation in the United States.
A judge in New York has heard that Rocco is living with his father in England.
Lawyers last week told Mr Justice MacDonald that Madonna wanted the teenager to return to live with her in the US and had issued an application in England under an international legal convention.
They said the singer now wanted to withdraw that application and bring the legal proceedings launched in England to a close.
The judge said last week that he had to decide whether the proceedings launched by Madonna in England should end - or whether he should make decisions on Rocco's welfare.
"It would be my fervent hope that discussions between the parties can reach an amicable resolution," Mr Justice MacDonald told the court last week.
"An amicable negotiated resolution is definitely the way forward and in Rocco's best interests."
Specialist legal teams are representing Madonna, Mr Ritchie and Rocco.
Madonna is represented by barristers David Williams QC and Jacqueline Renton; Mr Ritchie is represented by barristers Alex Verdan QC and Michael Gration; Rocco is represented by barristers Henry Setright QC and Edward Devereux via a court-appointed guardian.
Mr Williams last week told Mr Justice MacDonald that Madonna had launched proceedings in England under the Hague Convention on the Civil Aspects of International Child Abduction.
A judge in New York is analysing issues relating to the custody of Rocco - and those proceedings have already been widely reported in the media.
She has also urged Madonna and Mr Ritchie to reach agreement.
Madonna was not at Thursday's hearing - and was not at last week's hearing.