Use eyeshadow primer prior to puting on eyeliner! Make sure to put it on top of your lid, as well as underneath. 

Also, what kind of eyeliner are you using?

Be sure that you use an eye primer.  One I've been using lately is Palladio Herbal Eye Primer. 

Also, you may want to switch to a long wearing eyeliner or even a waterproof version.  A good one that I've been using lately is from Maybelline, called Master Drama.  Avon sells a good one too, Glimmersticks Liqui-glide eyeliner. 

If you still want to make use of your current eyeliner, try topping the eyeliner with a matching eyeshadow.  It helps the liner last longer.

Good luck!

If you are using a pencil, make sure it is really sharp! If using a gel, make sure your brush is clean and there aren't any stray bristles. When you do have smears, I recommend cleaning up with the Q-Tip precision tips.

My eye liner would always smudge and disappear by the end of the day, and I have tried soo many eye liners! I have used multiple waterproof eyeliners, tried setting it with eye shadow, used eye primer, and used q-tips to absorb the water before applying. However, I discovered a solution: Makeup For Ever Aqua Eyes eyeliner. I don't have to worry about my eyeliner budging at all any more!

I just bought the Urban Decay 24/7 Eye Pencil in Perversion... One swatch in the store was all I needed. You really have to scrub it off. I also use Kat Von D's Tattoo Liner in Trooper for any of my liquid needs. Haven't used a gel liner yet... I must admit I'm a tad bit scared of them. But these two are great in my opinion! I'm always on the hunt for a true BLACK eyeliner. None of that brown-black, blue-black crap... I want it BLACKEST BLACK!

Nars' Larger Than Life Eye Liner in Via Veneto is a very rich black that dries in 20 seconds flat. Most pencils like Urban Decay or Make Up For Ever will take about 2 minutes to dry. Also, the pencil does not smudge after 20 seconds. I dare you to mark your hand and try! 

My fave is Lancome artliner. It's a liquid liner. It literally stays put all day but you can reapply if needed. Takes some learning to apply it but well worth it.  One liner lasts for many months.  That's the one staple I have in my makeup.. havne't found many other products I'm that fond of

Before you're done applying? What kind of eyeliner is it??? I've only had that problem with liquid liner. Gel, pencil or powder liner doesn't usually have these issues, so switching formulas may help. Also, if the smudging is getting worse throughout the day, consider changing or not applying eye cream or moisturizer in the eye area in the morning, and/or try using eye primer.

I'd invest in a high-quality eyeliner. Something like Urban Decay's 24/7 pencils won't smear on you at ALL. These are pricey, so if you're not willing to invest in a new liner, you might want to use primer, because that reduces smearing and creasing no matter what you're wearing on your face.