I have a 1992 W140 S500 with 119 engine. It only make around 23,000 km. When it is hot or cold..... starting is not a problem. When I drive it for say 30
minutes and stop for say 15 minutes, then it is very difficult to start. When
it get started it is very rough. Any idea.

Possibly the distributor caps and rotors (there are 2 of each located on the front of each cylinder head under the big plastic covers).
If these are original, they may be age-affected, such as corroded contact points. It would be worth checking, the parts are rather pricey but not too bad to replace (labor). You could also consider replacing the sparkplugs if the serivce history is not known.

Gilly

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I have open up both distributor and clean both distributor cap and rotor. The problem goes away.
Thank you.