Hey, Thank you Larry! I do have the photo streaming activated, and I'll bet that's where the duplication comes from. I will follow up on that
To answer your questions, I use a Macbook Pro retina display 15-inch, running the latest version of OS X El Capitan -- 10.11.2 and Photos Version 1.3 I have iCloud storage service, but my understanding is that it stores only what I manually feed to it. I notice that the Cloud feeds photos from my computer to my iPhone -- and probably vice versa but don't know if that means there could be some sort of loop created where photos originating on the phone get sent repeatedly the Mac.
Again, thank you for the photo streaming point. I'll try to figure that out.