My 4 year old Bassett hound has recently started waking up and gasping for air for about 15 seconds then stops. He still eats but has started acting kind of lethargic. He never does it while awake only when waking up. Can someone please help me?

The best we can do here is guess, and those are pretty vague symptoms. So if you don't mind I'll ask a couple of questions myself.
First, Is his waking time normal for him or does he seem to be waking at odd times because he is in distress?
Where do you live and is he on heartworm prevention?
If his eating habits are normal is he losing or gaining weight?
Does he seem to "poop" out when he exercises or is he just generally lethargic?
Take his normals and weigh them against what you see now, things such as water intake, urinary habits, bowel movements, activity level etc.
Could be a number of things causing the lethargy, not sure about the gagging or gasping, it is hard to get a good image of exactly what you mean by those terms.
But you seem concerned about him, if the lethargy continues I would make an appointment to get him in to see the Vet.

I live in Lawndale, CA. He eats normal and drinks normal. I walked him an hour and he did not do it and seem fine. But when he sleeps he will wake up and do what seems like a panic attack. But after he is normal. He hasnormal bowl movments and goes pee regularly. He seems normal besides that.

http://www.veterinarypartner.com/Content.plx?P=A&A=2335
http://www.youtube.com/watch?v=1UyBrb0Hhpk

Just a wild guess, but check out these two links about reverse sneezing.
Is this what you are seeing and hearing?