Do you want both domains to go to the same exact site or both domains to go to two totally different web sites?

Well Google usually doesn't like duplicate content, but not sure how that would be weighed with doing versions for multiple languages.  I'll see what I can find out there and if anybody else wishes to chime in please feel free to do so.

Hi Mitch,

I just realize that Lunar Page don't use redirections for their domains, they have this:

http://www.lunarpages.com/
http://www.lunarpages.com.mx/

So LP use each domain to develop a website of the same company and in different language just as I wanted to do it. Interesting. Although LP also have:

http://www.lunarpages.co.uk/

Which is also in English and has nearly the same contest as http://www.lunarpages.com/
how's that? They are duplicating content, aren't them? Although they have a good PR in each domain, and just in lp.com use a favicon, why?
If I google web hosting, LP doesn't show up, so the little green bar it's not that important after all.

Thanks LeVampire, yes you probably right, I've received similar advice in others forums and got this example, it's the favorite of SEO guys, look what happens when you type the next links:

www.ibm.com or www.ibm.com.mx or www.ibm.com.es etc. It's amazing, they've redirected domains from all over the world to the same website.
Just wonder why LP did it in a different way?

Hmmm... I see, well thanks for take us in consideration first that's so nice from LP .

Anyway I have many doubts of all SEO stuff. Even I've been advised to follow ibm example, I've search some of the important words they got in their page and ibm doesn't show up in the results. Except of course for ibm itself .