Fakery also can ruin the credibility of search results for the social search engine that Facebook says it is building.
Colleen Callahan uses a pseudonym on Facebook to shield content from prospective employers.

But in October, another Facebook page for the hospital popped up. This one posted denunciations of President Obama and what it derided as “Obamacare.” It swiftly gathered hundreds of followers, and the anti-Obama screeds picked up “likes.” Officials at the hospital, scrambling to get it taken down, turned to their real Facebook page for damage control. “We apologize for any confusion,” they posted on Oct. 8, “and appreciate the support of our followers.”

The fake page came down 11 days later, as mysteriously as it had come up. The hospital says it has no clue who was behind it.

Fakery is all over the Internet. Twitter, which allows pseudonyms, is rife with fake followers, and has been used to spread false rumors, as it was during Hurricane Sandy. False reviews are a constant problem on consumer Web sites.

Gaston Memorial’s experience is an object lesson in the problem of fakery on Facebook. For the world’s largest social network, it is an especially acute problem, because it calls into question its basic premise.

Facebook says it has always taken the problem seriously, and recently stepped up efforts to cull fakes from the site. “It’s pretty much one of the top priorities for the company all the time,” said Joe Sullivan, who is in charge of security at Facebook.

The fakery problem on Facebook comes in many shapes. False profiles are fairly easy to create; hundreds can pop up simultaneously, sometimes with the help of robots, and often they persuade real users into friending them in a bid to spread malware. Fake Facebook friends and likes are sold on the Web like trinkets at a bazaar, directed at those who want to enhance their image. Fake coupons for meals and gadgets can appear on Facebook newsfeeds, aimed at tricking the unwitting into revealing their personal information.

Somewhat more benignly, some college students use fake names in an effort to protect their Facebook content from the eyes of future employers.

Mr. Sullivan said that since August, the company had put in place a new automated system to purge fake “likes.” The company said it has 150 to 300 staff members to weed out fraud.

In October, Facebook announced new partnerships with antivirus companies. Facebook users can now download free or paid antivirus coverage to guard against malware.

“It’s something we have been pretty effective at all along,” Mr. Sullivan said.

Facebook’s new aggressiveness toward fake “likes” became noticeable in September, when brand pages started seeing their fan numbers dip noticeably. An average brand page, Facebook said at the time, would lose less than 1 percent of its fans.