* Gaddafi sons' trial seen as test for Libyan state
* Saif al-Islam being held by former Zintan rebels
* Human rights groups allege shambolic justice in Libya
* Ex-Gaddafi officials say have inadequate legal counsel (Adds adjournment, quotes, courtroom colour)
By Julia Payne
TRIPOLI, April 14 (Reuters) - Libya opened the trial of deposed leader Muammar Gaddafi's sons and dozens of his ex-officials on Monday in a test of its transition to democracy, but it was quickly adjourned as some of the investigations had not been completed.
Neither son, Saadi Gaddafi and Saif al-Islam, was in court at Tripoli's Al-Hadba prison, but the late ruler's spy chief Abdullah al-Senussi was among the former senior aides sitting in blue jumpsuits behind a fenced-off section.
The defendants face charges ranging from corruption to war crimes related to deaths during the 2011 uprising against Gaddafi, who went on the run for months before being captured and quickly killed by rebels.
If convicted, some of them could face the death penalty.
The North African OPEC member has struggled to establish basic institutions and the rule of law as Gaddafi left behind a shell of a government after absorbing all the power into his own hands during his four-decade rule.
The International Criminal Court and other human rights organisations worry about the fairness of Libya's justice system although the government won the right last year to try Gaddafi's former spy chief at home instead of at the ICC in The Hague.
Saadi Gaddafi, known as a playboy with a brief career in professional soccer who was extradited to Libya from Niger in early March, did not appear in court because prosecutors said the investigation against him was unfinished.
Gaddafi's more prominent son, Saif al-Islam, remains in the custody of the powerful Zintan tribe in southwest Libya who have refused to hand him over to the central government, saying they believe it cannot provide a secure trial. Saif was only expected to appear via video-link.
The trial began a day after interim prime minister Abdullah al-Thinni resigned following an attack on his family and the ousting of his predecessor barely a month ago.
Proceedings were adjourned until April 27 to give investigators more time to prepare their cases and organise videolinks with the Gaddafi brothers and six defendants in Misrata who could not be taken to Tripoli due to a lack of security en route.
Post-Gaddafi Libya has so far been defined by a weak interim government and growing unrest, with former revolutionary fighters refusing to give up their weapons, and armed protesters blockading crucial oil exports.
Addressing the four judges, many defendants complained they had not been given access to lawyers or only saw them at court appearances. Reuters counted only nine lawyers, far fewer than the 25 defendants present.
"I want to be treated like other prisoners. I want visiting rights. I don't have a lawyer. It's not fair," said Senussi, who has been in prison for over a year.
Prosecutors said Senussi had been allowed to see relatives, but denied lawyers had been prevented from assisting clients.
Senussi was joined in the dock by Gaddafi-era prime minister Baghdadi al-Mahmoudi, former foreign minister Abdul Ati al-Obeidi and ex-intelligence chief Buzeid Dorda.
Sidiq Al-Sour, head of investigations for the prosecutor's office, said there were 36 ex-officials on trial. Four defendants had already been released, but not acquitted, and another was sick and unable to attend.
"This case has been riddled with procedural flaws right from the beginning, which have made it grossly unfair to the defendants," Richard Dicker, international justice director at Human Rights Watch, said in a statement.
Defence lawyers have been frustrated by delayed and constrained access to the thousands of pages of evidence. Human Rights Watch also said prisoners had no lawyers present during interrogations. Prosecutors said they only allowed lawyers to view the evidence in their offices to avoid its release to the public.
Libya's justice minister insisted the trial was open to the public and this would ensure the process was fair and not turn into a "Mickey Mouse" show trial.
"I will not allow any crazy stuff, I will make sure it meets international standards ... that is why we are having open trials," Salah al-Merghani told Reuters.
"We heard there were complaints from the lawyers ... The court will see if the complaints are genuine or not." (Additional reporting by Feras Bosalum; Editing by Patrick Markey and Alison Williams)