Dear Zinos,
Thanks for the post and sorry for the long delay in responding.
From 1929 until 1998 married men were not allowed to be ordained to the priesthood in the Byzantine Catholic Churches in North America. This was at the request of the North American Roman Catholic bishops who were uneducated about the Byzantine Churches and scandalized by the thought of a married priesthood. This past summer Pope John Paul II and the Congregation for the Eastern Catholic Churches (in Rome) restored this ancient right to the Byzantine Catholics in North America.
Since you are not currently a member of a Byzantine Catholic parish you might check one out (there is one in Minneapolis) and, if you find a spiritual home in the Byzantine Church you might want to join it. I would suspect you would need to be part of a worshiping Byzantine community for two or three years before you would be considered eligible for candidacy for the priesthood. This is because the lived experience of Byzantines and Romans is quite different and the time would allow you to evaluate and discern your vocation. You might also be interested in attending one of the regular Vocation Discernment Weekends at the Byzantine Catholic Seminary in Pittsburgh (the next one is the weekend of January 16-18, 1999 and their website is part of
www.byzcath.org [
byzcath.org]) or participating in one of the diocesan retreats (such as the Archdiocesan retreat during the third weekend of Greatfast - March 5-7, 1999).
If you have a bachelor's degree in any field it would be accepted as a starting point for the seminary. I suspect you would still be required to take the full 4 years of theology. To my knowledge there are currently no married candidates studying in the Byzantine seminary and I don't know what kind of facilities they would provide to a married candidate (I suspect an apartment in one of the diocesan buildings nearby would be available to a married candidate and his family). No training would be done in Europe.
For additional information please contact one of the priests listed on the seminary website - they all have e-mail addresses.