Members of the alt-right movement differ on many points, but are generally outspoken in their attacks on multiculturalism, globalisation and immigration.
Their targets include political correctness and feminism, and they have typically characterised themselves as being anti-establishment.
The election of Donald Trump – a presidential candidate supported by much of the alt-right – could change that.
He has appointed Steve Bannon as his chief strategist. Mr Bannon was formerly executive chairman of Breitbart News, a news site that specialises in coverage of the alt-right, but does not identify itself as part of it.
That has led some to speculate about whether certain alt-right views could soon become official US policy.
USA Today was one of the first mainstream news sites to report the suspensions.
Among them was Richard Spencer, the president of the National Policy Institute, which describes itself as being dedicated to the “identity and future of people of European descent in the United States”.
The NPI’s own Twitter account and that of its Radix Journal have also been barred by the platform.
Several of the accounts’ recent tweets had included the word “cucks” – a term of abuse used by the alt-right to disparage opponents. It is derived from cuckold and signifies the target is in some way weak.
It is not clear, however, whether this was related to Twitter’s action.
“[This] is corporate Stalinism in the sense that there is a great purge going on, and they are purging people on the basis of their views,” Mr Spencer said in a video he posted to YouTube.
“I and a number of other people who just got banned were not even trolling.”
He added he now planned to use Gab instead.
Mr Spencer was banned from visiting the UK earlier this year by the then Home Secretary Theresa May, who suggested his views would “foster hatred which might lead to inter-community violence”.
USA Today identified four other high-profile alt-right figures who had also been suspended.
The Southern Poverty Law Center – an Alabama-based anti-hate group – welcomed the news.
“Good riddance,” it tweeted.
The group said it had previously asked Twitter to remove more than 100 white supremacists’ accounts.
Twitter typically allows users accused of abusive behaviour to return after a temporary lockout.
However, it permanently banned Breitbart technology editor Milo Yiannopoulos in July, when it said he had helped incite abuse against the actress Leslie Jones.