Do you have any links relative to these libraries. I would be interested to know about them.
The tablets of Ebla (near Aleppo, Syria) provide an early example.
Here excavators found approximately 2,000 clay tablets dating back to 2300 b.c.e., recording information about food, clothing, and raw materials, apparently used as a palace archives. A similar cache was found at Ras Shamra, Syria, reflecting the 13th-century b.c.e. city Ugarit.
http://earlyworldhistory.blogspot.com/2012/03/ancient-libraries.html
http://eduscapes.com/history/beginnings/3000bce.htm