The Melkite Eparchy of Newton has a good series of articles about the Melkite Church’s concerns about Vatican II.
http://www.melkite.org/xCouncil/CouncilIntro.htm
Based on material on the Melkite eparchy’s website, the Melkites only accept the first seven councils as ecumenical
http://www.melkite.org/Challenge2007b.htm
1. What are the seven great meetings called that gave us the basic faith of the Church, and where was the first one held?
A Ecumenical councils, Nicaea
40. Was the Vatican Council an ecumenical council? Why? Why Not?
A The Vatican council was not an ecumenical council – no participation from the Orthodox
http://www.melkite.org/Challenge2007C.htm
22. What are the Ecumenical Councils?
The seven great meetings called that gave expression to the basic faith of the Church
http://www.melkite.org/Challenge2006C.htm
8 How many Ecumenical Councils were held?
a. Seven Ecumenical Councils
http://www.melkite.org/Challenge2005B.htm
Could it be because it was just for the western or Latin Church, VC II?