The Lindt Cafe siege gunman Man Haron Monis was a "radicalised terrorist" regardless of his lack of contact with Islamic State and his mental health issues, an eminent US terrorism expert said.

On Tuesday, Professor Bruce Hoffman told the Sydney siege inquest that the taking of hostages inside the Martin Place cafe "overwhelmingly met the criteria of terrorism".

Professor Hoffman, the director of the Centre for Security Studies at Georgetown University in Washington DC, said Monis had a political motive and his demands during the 17-hour siege were not monetary or personal but aimed to spread his message to a wider audience.

Although there is no evidence Monis had contact with Islamic State, also known as IS, ISIS, ISIL and Daesh, Monis's acts were "inspired" by the terror group, he said.

"In this expert's view, the case is overwhelming that it was terrorism," Professor Hoffman said via an video link from the US.

Under questioning by Jeremy Gormly SC, counsel assisting the Coroner Michael Barnes, Professor Hoffman said Monis's apparent mental health issues, including narcissism and delusions of grandeur, were "immaterial" to the question of terrorism.

"The act itself was a terrorist act," he said.

Notwithstanding this, Professor Hoffman said historically many terrorists, including suicide bombers, had mental illnesses and terrorist organisations preyed on such people to carry out their deadly acts.

ISIL employed a strategy to court "lone wolves", including the mentally ill, the deeply religious and recent converts, to carry out violence, without knowing or caring about the identities of the individuals, he said.

Professor Hoffman also cited Theodore Kaczynski, dubbed the Unabomber, who killed three people and injured 23 others in a bombing campaign in the US between 1978 and 1995. He was diagnosed with schizophrenia but is "widely accepted as a terrorist".

He said Monis "self-identified and self-affiliated" with ISIL and, following the siege, the terror group acknowledged his actions in its magazine.

The inquest on Tuesday also heard that other experts are expected to give evidence that says Monis should not be considered a terrorist.

In fact, Monis had come to be regarded as a "serial pest" to the Australian Security Intelligence Organisation after he provided numerous, useless tip-offs to the spy agency.

Forensic psychologist and radicalisation expert Dr Kate Barrelle said Monis was "atypical" in his motivations and behaviour compared with most people who are radicalised to the point of violent extremism.

Dr Barrelle said Monis was more of a "lone wolf", which is "very rare".

"Wolves are pack animals - it's the unusual wolf who radicalises alone," Dr Barrelle said.

Mr Gormly asked: "Did he behave like a terrorist in the siege?"

Dr Barrelle replied: "No.

"He behaved like someone who had backed himself into a corner."

Dr Barrelle said Monis spouted complex mixed messages and was erratic in his proclamations and this interplayed with his mental health issues, particularly his persecutory delusions.

"There is a high incidence of mental health issues in the lone wolf group of terrorists," she said.

Monis and two hostages Tori Johnson and Katrina Dawson were killed inside the Lindt Cafe in Martin Place in the early hours of December 16 last year.

Professor Hoffman has studied terrorism for more than 40 years. A third edition of his acclaimed 1998 book, Inside Terrorism, will be published next year.

The inquest continues.