Both movements tap into a toxic mix of resentment triggered by perceived societal decline, hatred of Jews, a global elite accused of conspiracies and a supposed need for purgative violence -- and use social media to build up their brands.

"They have common interests, if only in the wish to plunge society into chaos, a racial war or a war for civilisation," said Laurence Bindner, co-founder of the JOS Project, which monitors extremist propaganda online.

She noted "a pragmatic sharing of operational documents such as tutorials -- you find in far-right groups the same documents shared by jihadists."

Increased violence from neo-fascists like the Proud Boys, the Base or the Atomwaffen Division -- which Canada this week placed on its terrorist list of banned organisations -- compounds the challenges for governments already grappling with jihadist threats.

"The reason they're mobilising is that there is a sense of emergency. They're under threat and they're being persecuted everywhere so they have to act," said Thomas Hegghammer of the Norwegian Defence Research Establishment in Oslo.

Taking their cue from grisly videos of decapitations and other atrocities by Al-Qaeda or the Islamic State, far-right fanatics often film their attacks to embolden sympathisers.

The attacker who massacred dozens at mosques in Christchurch, New Zealand, in 2019 broadcast his attack on Facebook Live.

A few months later an anti-Semitic attack in the German city of Halle was streamed on Twitch.

"There is clearly an admiration of supremacists for jihadists. They even use the term 'white jihad' to explain what they're doing," said Colin Clarke, research director at the Soufan Group, a risk consultancy.

- 'Diabolical cocktail' -

Some white supremacists have even urged tactical alliances with Islamist forces, such as Norwegian Anders Behring Breivik, who killed 77 people in a bomb attack and shooting spree 10 years ago.

In his "manifesto," Breivik called for cooperation with Al-Qaeda, Al-Shabaab in Africa, and other "devout factions of the Islamic Ummah," or nation, to deploy nuclear or chemical weapons in Western Europe.

And last June, US officials revealed that an American soldier who was also a member of the neo-Nazi "Order of the Nine Angles," or O9A, based in Britain, had plotted to spur an Islamist attack on his unit in Turkey.

An admirer of Hitler as well as Osama Bin Laden, "Ethan Meltzer plotted a deadly ambush... in the service of a diabolical cocktail of ideologies laced with hate and violence," a New York prosecutor said.

When they are not trying to enlist help from jihadists directly, supremacists are copying their efforts to expand internationally to find recruits, raise money and test the waters for cooperation among far-right factions.

Analysts warn that such efforts will increase once Covid travel restrictions ease, as operatives try to meet in person to avoid digital surveillance.

"There will be more cooperation between members of these organizations, travelling to network and strategize in Europe and North America and reinvigorate fundraising through events and personal interactions," the Soufan Center said in a report Friday.

- 'Viral-minded' -

Similarly, jihadists are also keeping an eye on white supremacist groups trying to build up their base, underscoring the growing reality that tactics trump diametrically-opposed ideologies.

Last month, SITE Intelligence reported that an alleged Islamic State supporter was endorsing on social media a "tip" he picked up from a far-right discussion on line -- go learn to fight with Ukrainian militias fighting Russia.

"You can destabilize the whole European continent from Ukraine, with excellent strugglers who have the right logistics capabilities and vision," the jihadist posted.

For SITE's director Rita Katz, this cross-pollination of extremist strategies highlights the common push to attract a wide range of individuals to the most appealing terrorist "brands."

Just as IS drew from hard-core fundamentalists to criminals to impressionable teenagers, "today's far right is its own hodgepodge of extremist communities: militias, neo-Nazis, white nationalists, neo-fascist street groups, and conspiracy theory movements like QAnon," she told AFP.

"Rigid extremist ideologies are being replaced by viral-minded, hive-like extremist movements," she said, and "movements that are successful are the ones that create the most vast and active online infrastructures."

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