* Arrests peaceful in both cases
* Nashville arrests thrown out by court
AUSTIN, Texas Oct 30 (Reuters) - Dozens of protesters at economic inequality demonstrations in Austin, Texas, and Portland, Oregon were arrested peacefully early on Sunday over allegedly failing to comply with rules in each city.
Both protests were among many held across the country since September by demonstrators who say they are angry over economic inequality and what they see as Wall Street greed.
At Occupy Austin, some 38 people were arrested on Saturday night and early Sunday after refusing to let police take down food tables and clean the City Hall plaza where they had camped for several weeks, police told Reuters on Sunday.
They were charged with criminal trespass and issued citations that mean they can't return to the protest site.
"We've had a very peaceful Occupy Austin, especially compared to the rest of the nation, but we do have rules that have to be enforced," said Austin Police Officer Dennis Farris.
Makeshift encampments sprouting up in cities nationwide have forced local officials to tread carefully between allowing peaceful assembly and addressing concerns about trespassing, noise, sanitation and safety.
In Portland, protesters' attempt to extend their occupation to a third city park in an upscale downtown neighborhood was broken up by police early Sunday morning.
Some 25 protesters were arrested on charges related to rules about use of the park.
"It was peaceful, methodical and business-like," said police spokesman Pete Simpson.
Protesters at the Nashville, Tennessee, Occupy encampment were spared a curfew check on Saturday night after more than 50 arrests last week over curfew violations. They were released after a court official said there were no grounds for charges.
Other weekend protests struggled against the elements.
In New York, a day after authorities confiscated their generators, hundreds of protesters struggled to stay warm and dry Saturday after more than an inch (2.5 cm) of snow fell in the city.
In Washington, demonstrators marched in sleet to the U.S. Treasury to urge higher taxes on the financial sector, beating a drum and chanting "Banks got bailed out, we got sold out!" (Reporting by Karen Brooks in Austin, Dan Cook in Portland and Tim Ghianni in Nashville; Writing by Lauren Keiper; Editing by Jerry Norton)