What are the government styles and who are the current leaders of north and south korea?

The South Korean government's structure is determined by the Constitution of the Republic of Korea. This document has been revised several times since its first promulgation in 1948 (for details, see History of South Korea). However, it has retained many broad characteristics; with the exception of the short-lived Second Republic of South Korea, the country has always had a presidential system with a relatively independent chief executive.

The current leader of North Korea is currently Kim, Jong-Il.  

But, according to the North Korean Constitution, the "President for Eternity" is the long-dead Kim, Il-Sung, who died back in 1994. Their Constitution states no other person will ever assume the title of President of North Korea.  

North Korea is the only country with a dead person for President.