The skinheads were on two planes which arrived at Skavsta airport outside Nyköping at 6pm and 8pm on Friday evening.
The six men were the most disruptive in a gang of German skinheads who were on their way to the extreme right 'Salem march' outside Stockholm on Saturday afternoon, according to Swedish Radio Sörmland.
"There were several in the gang, but we didn't have the resources to deal with more than six," said Göran Risberg at Sörmland police to TT.
The skinheads were immediately deported under immigration law, on the basis that they were expected to commit offences in Sweden.
The march is an annual event held in the memory of a 17 year old boy who was beaten up and stabbed to death in Salem in 2000. The attackers had immigrant backgrounds. The event has become a focus not only for right-wing extremists, but also for anti-fascist protestors.
At 10.30am on Saturday the first demonstration began when a group of around 15 people from the local Left Party marched under police protection from the council building in Salem to Rönninge square. Member of parliament Kalle Larsson was among the speakers.
At lunchtime the Network Against Racism began collecting in Rönninge square for a demonstration.