The correct spelling of the town at the time your ancestors lived there is: Nagy-Becskereck, Torontal, Hungary. After WW I the name changed to Zrenjanin, Srbia.
There is a new web-site for Srbia that is very helpful for people doing their genealogy. The address is:
http://www.serbia-today.com/genealogy.html
When you read their site it mentioned that you can contact Mrs. Danica Radisic-Visnjic, which I did and had a responce in 2 days time.
I think she told me that some records may actually be located in Zrenjanin itself.
Good luck.
G. Bals