Let's define older, LOL.
I don't know if you mean just over forty or even older.
But to name just one, Kim Myung Min. I love this guy. Beethoven Virus is worth watching just because of him (although he was not forty yet).

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Kim Min Jong, my profile explains it, or at least no one under 35
Han Seok Kyu aka Master Kim from Romantic Doctor Kim.
I'm a fan of Kim Myung Min too though he's so cool haha.
My #1 favourite male actor is Oh Man Suk.  :)  He's currently 42.  

I've loved him in all the roles he's been in (that I've seen so far), but my 2 top faves are definitely The Vineyard Man and The True Colors.

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Jung Woo Sung (he's currently 44), still looking good tho
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Lee Duk Hwa- Age 65
After seeing him in so many dramas, I can't not like him
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Ji Sung (40 years) is an argument to watch a Drama even i'm not that interested in the story at first. He is a great actor and I think he even improved lately
   
AND
   
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Jo Dong Hyuk (40 years) - I don't feel attracted by older man BUT he just became hot since Bad Guys and Inspiring Generation

How old exactly... over 40... older? 

So Ji Sub