It doesn't have an alarm clock in the sense of having an alarm ring at a predetermined time. What it does have is a timer that will ring after a certain duration elapses.
I suppose if you were really good at clock-math, you could adjust the timer alarm to go off at the time that you wanted. Me, I'm terrible at clock-math, so I just use a regular alarm clock.
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ADDED - it's really even less useful as an alarm clock since the nano (6G) doesn't have an external speaker or vibrate function. You'd have to have your headphones on, or perhaps a speaker dock. But if you're going with a speaker dock, you might as well get one that has an alarm clock as well.