WASHINGTON — Robyn J. Skrebes of Minneapolis said she was able to sign up for health insurance in about two hours on Monday using the Web site of the state-run insurance exchange in Minnesota, known as MNsure. Ms. Skrebes, who is 32 and uninsured, said she had selected a policy costing $179 a month, before tax credit subsidies, and also had obtained Medicaid coverage for her 2-year-old daughter, Emma.

“I am thrilled,” Ms. Skrebes said, referring to her policy. “It’s affordable, good coverage. And the Web site of the Minnesota exchange was pretty simple to use, pretty straightforward. The language was really clear.”

The experience described by Ms. Skrebes is in stark contrast to reports of widespread technical problems that have hampered enrollment in the online health insurance marketplace run by the federal government since it opened on Oct. 1. While many people have been frustrated in their efforts to obtain coverage through the federal exchange, which is used by more than 30 states, consumers have had more success signing up for health insurance through many of the state-run exchanges, federal and state officials and outside experts say.

Alan R. Weil, the executive director of the National Academy for State Health Policy, an independent nonpartisan group, credited the relative early success of some state exchanges to the fact that they could leap on problems more quickly than the sprawling, complex federal marketplace.