Neither.

If I had to choose, I'd do the cool down to get more mileage.

i've been running alot as of late (55mpw during the last 4 weeks) and stretching is not part of the routine. during any run that involves a hard effort, i take a least 1 mile to cool down, then walk maybe a 1/4 to 1/2 mile. directly after the (harder and longer) runs, i take about 10 mins to Stick the (leg and hip) muscles.

i think that as long as you cool down gradually, you should not need to stretch.

I always try to do a 1k walk, then i use a foam roller in the evening, seems to be working for now.

I read this question and immediately thought of Jim Fixx.

If I had to choose one over the other, I'd go w/ a cool down run/decrease the heart rate rather than stretch. For some reason I'm thinking that if I tried to stretch immediately after a hard 10 mile run and still had a really high heart rate I'd be falling over trying to stretch with the body still wanting to have some form of locomotion (albeit at a slower/relaxed pace).

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Tad

It took awhile, but I finally discovered that its not the destination that's important, but rather the journey.

Important for what?

1. Your heart rate will gradually come down on it's own. No need to cool down.
2. Stretching is for improving mobility. Stretch if you need this.
3. Might be more beneficial to just add more run mileage in place of both if time is an issue.

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Simplify, Train, Live

I prefer the cool down. I stretch, but not regularly and generally well after the day is over during the evening.

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The secret of a long life is you try not to shorten it.
-Nobody

I prefer the cool-down as well.

During my xc running days, the coach never really enforced stretching but we were required to be diligent with cooldowns.

Benefits, as mentioned above:
-more mileage
-a general feeling of looseness upon finishing (HR comes down, muscles loose, no lactic acid buildup left)

Typical cooldown for me has more to do with the second point than the first. I jog super slow for about 1/4 mile, or spin easy for 3-5mins, or swim an easy 100-200 backstroke.

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"Don't you have to go be stupid somewhere else?"..."Not until 4!"

I think age is the biggest factor here. When I was in my 20s I could do neither and not feel a thing in my legs. Now I find if I don't stretch after an intense workout the discomfort lingers for a couple of days. If that's a non-issue just do a cool down to get those extra miles/kms in.

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"Train so you have no regrets @ the finish line"

Neither.

Do a bigger/better warm-up instead.

Post-run stretching is at best useless, and at worst detrimental (you get injured).

If you have to stretch (because you lack flexibility in general), do it outside workouts/races (not just before or after).

I haven't stretched since 2006.

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My Blog

My vote is stretch. I'm very strong with poor hamstring flexibility since birth.

I use to get "little" injuries (IT Band, hurt back, sore calf, tightness in the sole of my foot) all the time when running. I now stretch after EVERY single run. This is the most injury that I have been in ever.