Thank you for all your replies.  After receiving your reply Bigyin I looked on the internet regarding these insects.  It seems that the problem is rife in Spain.  I had never heard of it before, we moved to Tortosa only last year.   Strangely, our neighbour, chopped down his palm tree at the end of last year and I thought, how strange to chop down such a lovely palm - now I know why !!!

The problem now is how to get rid of the palms.  We could`nt afford a specialist as Bunter explained - is there anyway that we can do this ourselves.  Would chopping down and burning the whole thing work ?

I would be grateful for your suggestions.