Back to the vines from h*ll...(pictures)

Here's two pictures of the vines I was posting about a month ago...
http://www.hatrack.net/vines /
There may actually be more than one type of vine, but, these leaf shapes are the most prevalent...
I'd appreciate if anyone could identify this, it's an unwanted plant that's growing on our property, from the property next door.
Effectively, it's a network of underground and barely-surface vines. Diameters seem to range from reasonably slender (thinner than my pinkie) to thicker around than my thumb (and I have thick thumbs :)). They're sort of 'woody' looking, with a thin layer of 'bark', or outer skin of some sort. When snipped in half, they're a very clean white on the inside, with no rings of color. The bark/skin is similar to the texture of a very young sapling tree (thin and easy to 'peel' off). Very sturdy roots several inches into the ground, about every 4-5 inches along the length of the vines in/on the ground.
The vines will grow 'up' and climb around any items that they're given the chance to cover. In that case, they will produce shiny lighish green leaves (very small). They'll spiral around other plants (which will kill said plants as several individual shrubs in a short hedge have been killed by this wrapping).
The spiraling shoots seem to be a secondary product of the vines. Really, what they do is just cross and recross the dirt (non-driveway/concrete-covered) parts of our yard. Because they grow just under the surface of the soil (1" or so of dirt over them), or, _just_ along the surface, we didn't really notice they had effectively extended an interconnected 'net' of vines over our entire yard, till we tried to pull up 'some', and suddenly determined they were all over.
What I'd most like is targetted information on how to kill the vines. I did keep track of the previous answers, I'm just hoping for more information that will directly apply to this situation.
Gwen
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Wisteria - beautiful but vigorous invasive in some areas....we have all over central NJ.
--
Mike LaMana, MS
Heartwood Consulting Services, LLC
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On Wed, 2 Jun 2004 17:48:14 -0400, "Mike LaMana"

Thank you! While it doesn't actually do me any _real_ good good, having a name helps me to feel like I have a better chance of eradicating it.
Gwen
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The most effective way is to use something like 'Brushbgone'. I will take as much vine as is visible, coil it up, and then place it in a bucket of the stuff (mixed to strength) for a day or two. If the vine in question is particularly leafy, use Roundup in much the same manner.
Dave

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