It is believed Charlie Clift, five, and Kaiton Warnes, two, are in northern Cyprus with their mother Amelia Warnes, 23, from Eastbourne.
A judge at a court hearing in London gave permission for their identities to be revealed in the hope publicity will help find them.
Sir Gavyn Arthur said he had "grave concern" for the youngsters' welfare.
Lawyers believe the children are in Cyprus with their mother and her partner, Kaiton's father, Jason Warnes, 26, from St Leonards.
They have been missing since January 2014, but details of their disappearance have only just been revealed.
Lawyers said Charlie had been "abducted".
Charlie's father, Dominic Burt, 25, also of St Leonards, said he had not seen his son for months and he just wanted him back home.
Speaking at the hearing on Thursday, Sir Gavyn ordered the boys' mother and Mr Warnes to return the youngsters.
In a statement approved by the judge, lawyers said they were the subject of ongoing family court proceedings brought by East Sussex County Council social services.
Both boys were removed from the UK while on child protection plans and both were wards of court, they added.
The statement said: "His Honour Judge Sir Gavyn Arthur has asked for the assistance of the public in looking for these two young boys as there are serious concerns for their safety and welfare.
"If anyone has any information as to the whereabouts of these children please call Sussex Police."
Lawyers said the family were believed to have been in Lapta and Mr Warnes was thought to have been working in the hotel industry.
Two brothers from East Sussex who are at the centre of a family court case have gone missing, lawyers have said.