The East Timor government is in the International Court of Justice at The Hague, demanding the return of documents and data seized in the raids.
It says Australia took material vital for East Timor's case against the 2006 oil and gas treaty, which East Timor is challenging because of Canberra's alleged spying activity at the time.
East Timor says Australia has now seized the stronger position in that arbitration, and it's not convinced by assurances that the material won't be shared with those involved in the case..
Correspondent: Mary Gearin, Europe correspondent
Speakers: Joaquim da Fonseca, East Timor ambassador; Sir Eli Lauterpacht, lawyer acting for East Timor; Jose Guterres, East Timor's foreign minister
MARY GEARIN: East Timor came to the court armed with international lawyers, and outrage.
Its ambassador to the UK, Joaquim da Fonseca, says the countries are close friends, and last year's raids took Timor by surprise.
JOAQUIM DA FONSECA: It has caused deep offence and shock in my country.
MARY GEARIN: Sir Eli Lauterpacht, acting for East Timor, focused on the actions of a larger, richer, stronger nation versus that of a smaller, poorer one.
ELI LAUTERPACHT: This unprecedented and improper, indeed inexplicable conduct is not the behaviour of some state that does not subscribe to normal standards of international legal behaviour, rather it is the behaviour of a state of considerable international standing. Its behaviour in the present situation defies understanding.
MARY GEARIN: Sir Eli said the case was simple.
ELI LAUTERPACHT: One state has taken the property of another and should be required to give it back - untouched and without delay.
MARY GEARIN: Because Timor's challenge to the oil and gas treaty is behind closed doors in arbitration, this separate legal action to have the materials returned is the first public court stoush between the countries over the issue.
Timor used the international stage to reject Australia's argument that its national security could justify the raids, and it says the material in the hands of the Australians puts Dili at considerable negotiating and litigious disadvantage in arbitration.
Sir Eli again.
ELI LAUTERPACHT: The precise benefit to Australia of the acquisition of the information thus obtained cannot be estimated by Timor Leste. It undoubtedly must have given Australia an important negotiating advantage otherwise we must ask why would Australia have done it?
MARY GEARIN: East Timor's foreign minister, Jose Guterres, was there watching proceedings. He says that in the wake of this affair and the allegations of spying in Jakarta, Australia must change its approach to his country and Indonesia.
JOSE GUTERRES: We really want to work together as a partner, but the policies that have been going on for many years, you have to change it because it doesn't create trust between the neighbouring countries. No one will trust any country that does this kind of actions, whether big or small.
MARY GEARIN: Australia's counsel will have its turn next.