The National Democratic Party (NPD)—which the government has tried to ban—surged to 9% in Saxony, well above the 5% needed to enter parliament there.
In neighbouring Brandenburg, the German People’s Union (DVU) polled about 6%.
The results reflect anger at welfare cuts and disillusionment with persistently low living standards, says the BBC’s Ray Furlong in Berlin.
The ex-communists of the Party of Democratic Socialism (PDS) also did well in Brandenburg, but the mainstream parties still won in both states holding votes.
Voters in eastern Germany appear to have expressed their concern at the high unemployment they blame on Chancellor Gerhard Schroeder’s Social Democrats.
Our correspondent says the results are being seen widely as a no-confidence vote in Mr Schroeder, who brought in the welfare cuts with the blessing of the conservative Christian Democrats.
Fifteen years after reunification, east Germans still receive lower wages, benefits, and pensions than compatriots in the west of the country, and almost one in five is out of work.
In Dresden, the capital of Saxony, police clashed with demonstrators protesting against the far-right success.
The NPD’s 9% in Saxony means that the party has gained seats in a German state assembly for the first time since 1968.
It’s a great day for Germans who still want to be Germans,” said Holger Apfel, the NPD’s leading candidate in Saxony.
Despite having their majority eroded, Germany’s two mainstream parties remained ahead in both states, the early results suggested.
The ruling Social Democrats scored around 32% in Brandenburg, while the conservative Christian Democrats won 41% of the total vote in Saxony, the results showed.
Average unemployment in east Germany has been stuck at about 20%—nearly twice the national average.
Some six million people were eligible to vote in Sunday’s elections in Saxony and Brandenburg.
Germany’s government has described the NPD as a latter-day version of Hitler’s Nazi party and tried to ban it last year—a move rejected by the constitutional court.
The PDS scored their best election result ever, with 28% in Brandenburg.
However, they are unlikely to form a government in the state, which is ruled by a coalition of the Christian Democrats and Social Democrats.