This may seem like a simple question, but I have not really been able to find a good answer yet.

Recently my gluts have been getting more sore after during run or after during hill climbing on my treadmill. For example, yesterday I ran 35 minutes and the did hill climbing on my treadmill at 4.0 MPH and 10% incline for 35 minutes. Today, my gluts are really sore. Is that normal or am I lacking proper muscle support in core? I also notice I clench a little in the gluts when running even though I internally think about relaxing them if I feel tight there. I have been trying to do additional stretching of my hip flexors before and after running, but this does not seem to relieve the soreness in the gluts. I am planning on running today for 1 hour in about an hour so would like some advice if you have it on additional stretching or types of strength training that would help with relaxing the gluts.

Try stretching longer and work your hips and full lower abdominal area not just your gluts. check out www.livestrong.com also you can do some leg presses lunches planks etc these will all work with your lower abdomen/gluts and legs . one thing that might help is to get a tennis ball and sit on the edge on your couch and just roll the ball on the sole of your foot it will strengthin those muscles in your feel and shins.

Sounds like you're suffering from a bad case of tight fitting underwear.. Just kidding sounds like your working out hard being a little sore I imagine is normal

Completed my run and felt a bit "rusty" from sore glut. Strange problem to have, but I do feel better post run then pre-run so that is worth it.

I ended up doing a really long pre run jog (10 minutes) and also extra stretches. The aches did bother me psychologically more then physically while running. Thanks again on your suggestions. I am going to give myself more of a recovery ( no crazy hill climbing or back to back runs) in between the running days.