Edging problem "thin white line" between paths in Illustrator CS4...

I am making a map of Europe with Illustrator CS4 for a documentary about WWI and how the Versailles Treaty carved up imperial Germany. After having traced imperial Germany before Versailles, I then carve out the territories given to neighboring states. The problem is these very fine white lines that appear between paths.
I have two paths right next to each other. But for some reason I see this very thine white line gap that shows up between them and becomes much more evident when I export into Photoshop. Please notice this very fine white line in the black image. What you see in this image are in fact two paths side by side. There should be no line between them. And I have no idea why this very fine line appears but it gets much worse in Photoshop much more noticeable. Please click on image to see the line more clearly.
Thank you very much in advance for any help or suggestions.
- Nick

Dear Jacob and Peter,
Thank you both very much for your help.
Please see these photos showing my problem more clearly.
I am using Illustrator to draw the regions, Photoshop to consolidate the layers, and Apple Motion 4 to build my animation.
[1] : Imperial Germany in 1914.
[2] : Germany after Versailles.
In Illustrator CS4, the images [1] and [2] have the colored layers in "Multiply" transparency mode. It's how I want the layers to look when I import them into Apple Motion 4.
My idea was to color all the layers black in "Normal" mode and then apply "colorize" filters in Motion 4 and set the transparency to "multiply" in Motion.
Now with Imperial Germany (all layers colored in black with transparency set to "Normal"), when I bring the image into Photoshop, I suddenly get very fine white lines between the layers and these lines show up in Motion which is the big problem. Like I said, when you click on this last photo, and you see the image full size, you can clearly see the problematic lines which appear exactly where the layers touch each other. In the photo below, the territories ceded to Poland (West Prussia) and Lithuania (Memel) are not yet red. They are still black but you can see the lines.
I don't understand because in Illustrator there were no gaps whatsoever between the layers. In Illustrator CS4, I simply cut the "territorial losses" from imperial Germany using the "Trim" function in the Pathfinder Menu. I created the red and yellow layers from the original single "imperial Germany" layer. In Illustrator I can colorize all the layers black and still never see any gaps. The fine white lines, appear in Photoshop and in Motion.
(NOTE: The documentary is being in edited in Final Cut Studio which is why I use Motion for animating.)
Sorry to ramble on. Thank you again for any further help you can give me.
- Nick

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