Integrate the dropbox in my application which show security alert

Just a guess, but I think this might happen if you tried to reuse the app key and secret from the sample app in your own app, rather than creating a new application via https://www.dropbox.com/developers/apps/create and using that key and secret.

I know this is an old question but there is another possibility that has just bitten me so for future users who may hit the same issue:

If in the process of authenticating you run into an error message like "Another app on your phone may be trying to pose as the app you are currently using." it means more than one app installed on the phone has a callback activity registered for a single app key. You can fix this error by deleting one of the offending apps or by switching to a new app key.

I hit this issue by having different versions (debug & release) of the same app installed.

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