The International Criminal Court (ICC) in June charged Saif al-Islam Gaddafi with crimes against humanity over the killing of civilian protesters in February.
Following his arrest in Libya, the country has the right to put him on trial there. The ICC will only act if a country is unable or unwilling to investigate or prosecute, for instance when its legal system has collapsed.
Libya's prime minister on Saturday promised a fair trial for Saif al-Islam, who was captured in the southern desert.
We assure Libyans and the world that Saif al-Islam will receive a fair trial ... under fair legal processes which our own people had been deprived of for the last 40 years, Abdurrahim El-Keib said.
The Hague-based ICC began investigating Libyan violence after the U.N. Security Council referred the country's crisis to the court in February.
If Saif al-Islam were to go on trial there, he would be transported to a detention centre in a residential area of The Hague which the ICC shares with the U.N. Yugoslavia war crimes tribunal and the Special Court for Sierra Leone, where former Liberian president Charles Taylor is on trial.
With no police force of its own, the ICC has relied in the past on state cooperation to have its suspects arrested and many of them have remained fugitives such as Sudan's President Omar al-Bashir whose government has snubbed the court.
The Dutch authorities provide assistance to the Hague-based courts in the transfer of suspects to the detention centre, such as when former Bosnian Serb military commander Ratko Mladic was flown to Rotterdam on a Serbian government plane.
The detention centre is built next to an old prison where Dutch resistance fighters were imprisoned by the Nazis and inmates have single-occupant cells about 10 square metres in size, where they can watch TV, read or work on their cases.
If he arrives in The Hague, Saif al-Islam would be required to appear in court for an initial hearing, where he would be formally charged and informed of his rights.
ICC prosecutor Luis Moreno-Ocampo accuses Saif al-Islam of drawing up a plan to kill protesters and organising the recruitment of mercenaries.
After the initial hearing, a confirmation of charges hearing takes place. This is followed within 60 days with a decision on whether the suspect will be ordered to stand trial.
A trial can take years.
Congolese war crimes suspect Thomas Lubanga, the first person to be tried by the ICC, had his initial appearance in March 2006, followed by a confirmation of charges hearing eight months later. His trial started in January 2009, hearings ended in August this year and a ruling is still due.