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The decision by Dropbox this month to appoint Condoleezza Rice, the former secretary of state, to the company’s board of directors sparked a heated online debate about her views on Internet surveillance and the role of the National Security Agency.

And the debate doesn’t seem to be going away.

Protestors set up a website called “Drop Dropbox,” which says the appointment of Ms. Rice is “deeply disturbing.” The site is encouraging people to switch to competing cloud storage services.

One of the main arguments against Ms. Rice is based on a 2005 television interview in which she defended the N.S.A.’s warrantless surveillance program.

In response to the controversy, Drew Houston, chief executive of Dropbox, wrote a short post on the company’s website defending the decision to add Ms. Rice to the board.

“There’s nothing more important to us than keeping your stuff safe and secure. It’s why we’ve been fighting for transparency and government surveillance reform, and why we’ve been vocal and public with our principles and values,” Mr. Houston wrote. “Dr. Rice understands our stance on these issues and fully supports our commitments to our users.”

But some users of the service didn’t agree with the appointment, or Mr. Houston’s response to the criticism.

“OK. Good luck with that. Still dropping you,” wrote one person in the comments section of the Dropbox blog post.

“Actions speak louder than words,” wrote another customer, who also noted plans to stop subscribing to the service. There were hundreds of similar comments.

The Drop Dropbox website has been particularly vocal online, urging people to share the hashtag #DropDropbox and posting controversial videos of Ms. Rice and articles about her time in President George W. Bush’s administration.

On Twitter, the hashtag #DropDropbox has been shared by thousands of people, with some users pointing to video clips of Ms. Rice, and others saying they were closing their accounts on the service and jumping to alternative cloud storage providers.

“I am off. Bye bye, Dropbox #DropDropbox,” wrote Robert Brandl, a German web entrepreneur.

“Services owned by @Dropbox: Loom, Carousel, Mailbox, Zulip, Hackpad, Readmill,” wrote a person identified as Dr. Dave on Twitter. “Avoid if you value human rights! #DropDropbox.”

Dropbox in recent months has been adding to its product line and expanding globally. This month, the company released a new photo-storage platform and acquired Loom, a cloud-storage company and Hackpad, a service for organizing online documents.

In February, Dropbox raised an additional $350 million in venture funding, raising its valuation to $10 billion. The company is expected to file for an initial public offering within two years.

While it’s highly unlikely that the outcry will result in a reversal by Dropbox, it is providing a marketing opportunity to some of its competitors.

Sync, a Canadian company with a similar service, wrote on Twitter, “It’s like Dropbox but with real data privacy.”