my floor is built on I beams (2x3 top and bottom with an 8 inch by 7/16 chipboard between them )
It is covered with 5/8 inch plywood ( supposedly with glue between plywood and I beam ) then nailed.
The problem in question is, that floor is finished with ceramic tiles and now various parts of the floor started squeaking.
How do I eliminate that nagging squeak ?

Joe

Do you have good access to the underside of the floor from the basement? Sure hope you answer yes.

Yes I do > fortunately it's all open

I would suggest products such as this. Squeaky Floor Repair, Specialty Fasteners, Fasteners - McFeely's (http://www.mcfeelys.com/squeaky-floor-repair) Especial the $5.95 Sqeak Relief since you have access.