How do I convert a x86 RPM to a x86 DEB within a x64 system?

The process is quite easy, in short you need to modify the control file and that's it.

sudo alien -g package-name.rpm
cd package-dir/
sudo vi debian/control

Now change the architecture (i386 in my case) to be the one you need. For example, I added the amd64 archicture and this is how the line ended up:

Architecture: i386, amd64

Last step:

sudo debian/rules binary

This will produce the .deb file.

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References:

• Using Alien to convert .rpm packages to lpia .deb

I made it work with just this command:

fakeroot alien --target=amd64 package.i586.rpm