why I don't choose "multinational" or "national"
国际性的河流---- it implies that this river crosses more than one country. Trans- this prefix has a meaning of "穿过", which fits in this comtext perfectly. That is why I prefer it to the others.

pls refer to the following links for some examples of this usage

http://72.14.253.104/search?q=cache:1KAMM1MkUNsJ:www.creditw...
http://72.14.253.104/search?q=cache:BnP3ogTHucEJ:www.ipcri.o...

http://72.14.253.104/search?q=cache:vdfLhWaeeyIJ:www.eloiseg...
http://72.14.253.104/search?q=cache:VVtIK2GCIxkJ:www.sdnpbd....
http://72.14.253.104/search?q=cache:JJ9_sNg0JEUJ:ag.arizona....

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Note added at 1 day1 hr (2008-01-03 14:36:13 GMT)
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To Franksf:
transnational river --- it draws up an image of a river in motion---- FLOWING ACROSS.....
multinational or internation river--- the image of that river is static.
secondly, in terms of usage, the term of "transnational river" is more conventional as you can see in the examples quoted above.

Thanks again for your comment, I like this kind of discussion.

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Note added at 1 day15 hrs (2008-01-04 04:13:36 GMT)
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To Franksf:

inter- : it implies the relationship between or among things, just take the sample terms you mentioned; interprovince highway, interstate highway, or interstate phone calls etc. and interaction, all these phrases or words reveal a two-way relationship. a interstate highway it cannot be only one-way, it is a highway connects two or more cities, also a interstate call it involves two parties, the caller and the receiver, a conversation between them.
interaction and transaction are the examples in point. interaction involves at least two parties, they interact each other. put it in Chinese is "相互作用，不是单向的，而是双向的”。
while transaction can be one-way, say A transfers a fund into B's account. this transaction is one-way. also translation, it is from one language into another language, it is one-way transfer.

No longer ago, there was a post about “跨国公司”。 I prefer "transnational company" to "multinational company", trans- implies the action of crossing the borders, implies the expansion of the business. in this sence, multinational only means this company run its business in more than one country.

While the term of "多国会议/国际会议”， I prefer "multinational meeting or international meeting" to "transnational meeting", considering the context has no indication of motion--- crossing the border etc. The meeting normally is held by a host country where the place is fixed, it only means those who attend the meeting are from different contries around the world.

Thanks again and again for bringing up such meaningful discussion. Really I enjoy a lot.

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Note added at 1 day15 hrs (2008-01-04 04:16:18 GMT)
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No longer ago--- spelling error, should be not long ago. sorry.

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Note added at 2 days4 hrs (2008-01-04 17:24:30 GMT)
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To Franksf: You said "Inter-" is not limited to binary, there are many-body interactions for sure. I would not call Internet trans". ---Sure! that is what I mean. I did not say "inter-" is limited to binary.But I said " interaction involves AT LEAST two parties, they interact each other. " ---, " at least two parties" which means it can be more than two. in other words, as you said " is not limited to binary".