If you jog regularly, chances are good no matter where you live that you own a favorite pair of jogging pants to wear as an outer layer. In cooler weather, you're likely to keep these on for the duration of your workout, whereas if you're in a hot-weather climate, you might wear them to the track or other destination and shed them once you get there. In any event, what you wear underneath the jogging pants depends on your goals and tastes.
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If you're not planning to keep your jogging pants on throughout the run, and intend to shed them after a warm-up jog or stretching session, running shorts are an obvious choice for a second layer. Most running shorts nowadays have a built-in brief for men and women so that you don't have to wear a third layer underneath. A quality pair of running shorts will have a "wicking" fabric that draws moisture away from your body, thereby preventing chafing.
If you're doing a workout in weather that is too cold for shorts, or simply prefer the feel of having your legs hugged tightly throughout their length, then running tights are a good under-the-jogging-pants option for you. Writing for "Running Times," Adam Chase reports that running tights may offer improved muscle stability, muscle temperature regulation, enhanced blood circulation and protection from the sun's ultraviolet rays. Running tights come in a variety of materials, so you'll want to try on a range of examples to see what's most comfortable before deciding on a purchase.
Constituting a compromise of sorts between traditional running shorts and running tights, compression shorts -- which resemble traditional biking shorts -- have become increasingly popular among both elite and recreational runners. The length of these can range from very short, in which case they are known colloquially as "spankies," to knee-length; as always, the type you select is a function of your individual comfort and preference. Compression shorts are purported to warm and stabilize the thigh muscles, though this claim is, as of 2011, anecdotal.
If you have no plans to shed your jogging pants at any time during your jog, then there is no need for any special layer underneath them. You can wear whatever you would wear underneath any other type of pants, with caveats. Regardless of your sex, you'll want to apply some petroleum jelly or similar lubricant to the points at which your panties or briefs meet your skin; otherwise you may suffer significant chafing. Running specialty stores and catalogs offer men's and women's cold-weather running briefs offering wind-resistant properties.