Impeachment is an American thing.
http://www.honduras.net/honduras_constitution2.html
The Honduran Constitution reads:
Chapter VI, Article 237: The presidential term is four years... (No right to succeed himself.)
Article 239 ? No citizen that has already served as head of the Executive Branch can be President or Vice-President.
Whoever violates this law or proposes its reform, as well as those that support such violation directly or indirectly, will immediately cease in their functions and will be unable to hold any public office for a period of 10 years.
Chapter 10, Article 272:
The Armed Forces of Honduras are ... established to defend the territorial integrity and sovereignty of the Republic, keep the peace, public order and the rule of the Constitution, the principles of free suffrage and alternation in the presidency of the Republic.
Claro?
Before you claim that there are impeachment procedures in the primary document, be aware that, under Honduran Constitutional law, Article 239 holds precedence and by immediately rendering Zelaya an ordinary citizen he was not privileged to go through any impeachment whatsoever - he was automatically not El Presidente.
Though the legislature and the Supreme Court validated this, they actually did not have to. It is the responsibility of the military to do what is necessary to protect the country and specifically the principle of "alternation." The power stemming from a history of other attempts to seek the tile "El Presidente For Life."
Can't stay and play, my plane awaits!