How to understand if an opponent is going to reach Cultural Victory?

I usually play at Civilization IV with difficulty set to Prince, length set to Marathon and size of the map to Huge.

The problem is that happens quite often, in the 20 century, that an opponent win the game by reaching the Cultural Victory.

How can I understand that an opponent is going to win in this way and what can I do to impede his/her victory.

Solution 1:

If you go to the Victory Conditions screen (I believe it is F8) it should show you what is required for a cultural victory based on your game length. The left hand column shows how close you are to each condition, but the right hand column should show which of your opponents is closest. So you can watch this to see if they are gettting close to a cultural victory, and if so, attack the cities as mentioned in the other answers.

Solution 2:

The best way to stop an opponent from winning with cultural victory is to attack the city or cities of theirs which are producing the majority of that culture, and to do so early enough that you're able to pull it off. As @freegame says, it's the cities with the world wonders that you've got to watch out for because they produce a lot more than a normal city, even with national wonders involved. And also remember to capture religious founding sites; the wonders associated with them are always good, even for militaristic approaches, because of the amount of cash they tend to bring in.