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Donald Trump's inaugural speech did not go off without a hitch -- there was a clear fumble by the military -- but everyone's clammed up.

Trump began speaking and a minute and a half later, 8 men in uniform walk the steps and flank the prez from behind.

You see in the video, they stand motionless for 40 seconds when another man in uniform appears, clearly whispers something to the effect of, "We gotta get outta here STAT," and they quickly leave.

We've made a ton of calls to the military and no one's giving us an answer. Several of the people we spoke with say it was clearly a misstep for the guys to come out, but they won't say how it happened.