Why would a guy that is attracted to you gaze at your eyes and lips and smile for a long period without saying anything ?

He is:
1. fascinated with you and infatuated.
2. completely bumfuzzled at the prospect of talking to you.

Does this happen in class or at work? You can end it by going up to him and saying “Thanks for smiling at me, but if you don’t talk to me I will never talk to you or go out with you. So stop being a stalker, and either talk or knock it off.”

He was most likely thrown off guard by your looks, found himself distracted and stunned by your physical attractiveness and was maybe checking out your lips to see what they look like because he wants to kiss you.

They’re smitten by your charms combined with yet-unmanaged hormones.
He can be quite under the influence of natural love drugs in his bloodstream.
A more gallant fellow will try to have something interesting to say as his eyes melt into your incandescent beauty.
If he tries to wrench his attention away from the rush of endorphines caused by your image on his vision receptors, but he fails, we might understand. But some guys are helpless and some forget to try.

Note that there are at least three thing going on, and maybe you’re not uncomfortable with both.
Hard-Wiring… one’s visual attention is compelled for evolutionary reasons to respond to features that indicate reproductive viability. There’s just no way around the fact that the attention of our eyes can be commandeered by raw instinct to observe an inspiring profile. Being able to do something besides lingering on the view is an essential part of maturity. (But don’t lose the art a good linger, it’s good for you.)
Inspecting… the eventual assessment of everything about you. If he keeps this up you won’t have any secrets in a few hours. If nothing else an exclusive focus on you doesn’t let you learn much about him, beyond sharing his helpless. ...And inspecting can seem so much like oggling that it’s creepy.
Admiring… him admiring you can be a good thing for both of you to share. He likes you, and he’s doing everything he can to resonate with a positive response from you. He wants you to like him.

But I see zen has played through (d’oh! I took too long…) with an insightful response and the request for detail.
And @lookingglassx3 gets more specifically hits the nail on the head.

You already answered the question yourself so this is pointless, obviously he is attracted to you as you clearly stated in the question. Hm….so maybe the way your eyes and lips looks make him happy hence the smile. If you’re made so unhappy by it, stop hanging around him.

I’m betting he’s afraid of being rejected… and apparently, his fear is not unfounded.

He sounds smitten. Are small song birds flying around his head or little pink heart-like-bubbles bursting near him? Does he also sigh deeply and hang on your every word?

Clearly he is stunned by you.

When a teen boy is smitten, he often cannot think, so he stands there staring with this vacuous smile. If it makes you nervous, then he is not for you. Ignore him. If you do like him, then approach him, slap him lightly, and tell him to call you and ask you for a date. Or if you’re modern, tell him to Facebook you for a date. But I think it would be better if he was more formal.

Ok. You don’t have to slap him.

… oh ! Would this happen to be while he’s listening to you?
He might be learning how you express yourself so he can understand you more.

I also think it’s not a bad sign that his gaze is stuck on your face if that means it’s not stuck on some other part(s) of you. (Inspection gone wrong.) There is at least some level of respect going on.

Attraction. Tell him his staring makes you uncomfortable.

I do this a lot when I fall in love. I try not to do it to someone I’m not close too. But I love eyes so much.

You’re describing something that’s often called “leering.” Trust your instincts.

@SadieMartinPaul I don’t leer. I smile gently and with love, but I have an intense look. And I try to be gentle.

@Adirondackwannabe I send ten thousand apologies. I wasn’t referring to what you described; I was answering the original question.

You talk about your behavior when you fall in love—always a wonderful thing. In contrast, @christina30 described a guy who’s “attracted” to her and seems to stare nonstop. The two situations are different. @christina30 knows that there’s something off about this guy’s behavior—she’s uncomfortable—so I encouraged her to listen to her feelings.

Peace, brother, and no offense intended.

@SadieMartinPaul No offense taken. I was just thinking how I do this with a loved one. Yeah, it is creepy with a new person.

@Adirondackwannabe Thank you for understanding. I think you’re terrific, and I wouldn’t want to upset you…especially over a simple misunderstanding of who’s talking to whom about what.

Yes, I often stare adoringly at my husband, because I love him and can never get enough of him. If I did the same thing to a strange man, however, my name would be Mrs. Creepy!

May you go on loving and gazing.

@SadieMartinPaul Staring into a loved one’s eyes is one of the best pleasures in life. Being stared at by a stranger creeps me out too. You’ll also find not much upsets me. I have a few buttons, but I keep them under control usually.

Ask him why? Tell him he looks weird when he does that.

Indigestion. He wanted too hurl, but he didn’t want to have you see him do it.

He may have also been reluctant to move as he was waiting for the erection to subside.

It’s because seeing you makes him happy. Eyes: because he finds beauty and peace within them. Lips: because they are soft and hopes to feel it maybe one day. Of course you could always tell him it makes you feel uncomfortable, but if you do it make sure you say it in a nice way. He admires you, tries to capture the beauty he sees.