Police in the eastern German city of Halle have begun at least 10 inquiries after a Monday demonstration in which protesters used Nazi symbols and slogans.
Police say they are also investigating incidents in which some protesters attacked police, spitting on them and scuffling with them.
About 450 people protested as part of a series of demonstrations across eastern Germany. The demonstrations followed recent incidents in Chemnitz and Koethen, where two Germans died after encounters with immigrants.
Most of the marches have been protests against the presence of immigrants. The number of immigrants in Germany has risen dramatically since 2015 under the government's open-door policy towards people fleeing war zones and other conflict-affected areas.
But there is concern that the anti-immigrant movement is becoming a breeding ground for neo-Nazi sentiments. Members of right-wing organizations urged a strong turnout on Monday.
Police said they are investigating cases where marchers displayed symbols of banned organizations; performed Nazi salutes or called out "Sieg Heil" (Hail Victory), a phrase commonly used by the Nazis.
Authorities said many of those marching appeared drunk.
But they were quick to point out that they could not say if all the people marching in Halle belonged to right-wing groups. They also noted that a counterdemonstration drew in more than 80 participants but that there was no violence reported in relation to their protest.