I think that the question could be more easily answered if the specific nation was mentioned.  In approaching this answer, I looked at "President" as being critical.  Focusing on nations in 1990 who had leaders considered "Presidents" might have some limiting function in such a wide task.  If we are looking at the United States Presidency, then George H.W. Bush, the nation's 41st President, could be considered as a President in 1990.  Elected in the 1988 election over Democrat Michael Dukakis, 1990 saw Bush in the middle of his term.  Another President in 1990 could be found in Poland.  Lech Walesa, the leader of the Polish Solidarity movement, was elected as President of the Republic of Poland in December of 1990.  The nation of Slovenia, emerging from Communist control, held its first open elections for President.  In April of 1990, Milan Kučan won the nation's election for President.  He could also be considered as the President in 1990.   Without a specific nation, these are three options to the issue of who was President in 1990.