At least 28 young soldiers are shown on the internet in photos brandishing swastikas and making Hitler-style salutes, according to a report from SonntagsZeitung, the German-language weekly.
Among those are men with officer positions in the military hierarchy who appear to be unhindered by their behaviour, the report says.
It cites the case of a 20-year-old gunner who sports a tattoo of an imperial eagle with a black swastika in its claws.
The newspaper says the man is an active member of the international Hammerskins, a white supremacist group, which organizes regular combat training for its members.
It says at least 27 other soldiers have flaunted their neo-Nazi sympathies online.
The report cites the case of one recruit who was promoted to sergeant despite his public espousal of the belief that whites are superior, his support of “weapons fanatics” and the hanging of SS flags on his bedroom wall.
Dominic Lüthard, chairman of the extreme-right nationalist party PNOS, is one of the soldiers allegedly glorifying Nazi images.
Lüthard completed a training course with mountain infantry last year without any intervention, SonntagsZeitung reported.
He is scheduled to return to the army for obligatory service next March.
A variety of politicians of all stripes have called on such people to be immediately kicked out of the Swiss military.
Chantal Galladé, chairwoman of the parliamentary committee on security policy, declared that these men "pose a security risk”.
MP Hans Fuhr, a member of the right-wing Swiss People’s Party, agreed that the situation is a security problem that needs to be taken seriously.
However, for the Swiss army, the situation is not that clear-cut.
There is no legal basis that allows the army to exclude a soldier for preventive reasons, spokesman Christoph Brunner said.
Brunner also sought to minimize the magnitude of the problem.
Given that the army has 140,000 active members, the neo-Nazi issue is one of “very low intensity”, he told SonntagsZeitung.
The public use and dissemination of racist symbols is forbidden in Switzerland, following the introduction of an anti-racism law in 1995.
However, a clause states that the display of offensive symbols such as the swastika is only banned when they are used to promote a corresponding ideology, a correlation that is often difficult to prove.
For example, Nazi war flags cannot be confiscated at the Swiss border if the owner claims not to be spreading propaganda.
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Politicians have called for a closure of the loophole but the law has yet to be amended.