Dear Eric and Donovan,
Thanks for helping me, it worked!!!
I needed the average raster value to be an attribute of the polygon, so I used Zonal Statistics as Table tool in Spatial Analyst as Eric pointed out. It performed perfectly when I selected a subset of species (about 100 species, which means more or less 600 polygons). When I run for all species together it doesn't calculate for all polygons. I�??m afraid it is because of the overlaps. Thanks a lot for taking your time; any additional thoughts are welcome.
Thanks guys,
All the best.
Gui
PS. Donovan, I tried "extraction by polygons" but I wasn't able to find a way to add a polygon layer, only to enter x,y coordinates for one polygon only. Am I missing something here? Thanks a lot.