COLUMBUS, Ohio — First Wisconsin. Now Ohio and Indiana.

Battles with public employees’ unions spread on Tuesday, with Republican-dominated Legislatures pressing bills that would weaken collective bargaining and thousands of pro-union protesters marching on Capitol buildings in Columbus and Indianapolis.

After a week of upheaval in Madison, Wis., where the thumping din of protesters has turned almost celebratory, the battle moved to Ohio, where the Legislature held hearings on a bill that would effectively end collective bargaining for state workers and drastically reduce it for local government employees like police officers and firefighters.

Several thousand pro-union protesters filled a main hall of the statehouse in Columbus and gathered in a large crowd outside, chanting “Kill the bill,” waving signs and playing drums and bagpipes. There were no official estimates, but the numbers appeared to be smaller than those in Madison last week. One Democratic state legislator put the figure at 15,000; local papers reported crowds of about 5,000.

In Indiana, nearly all of the Democratic members of the state’s House of Representatives stayed away from a legislative session on Tuesday in an effort to stymie a bill that they say would weaken collective bargaining. By late Tuesday, they seemed to have succeeded in running down a clock on the bill, which was to expire at midnight. Representative Brian Bosma, the speaker of the Indiana House, said the bill would die when the deadline passed.