Hallo:
I'd like to know if it's possilbe to install Linux on external SSD and run it in two different computers. Of course, not at the same time. Just connect SSD to one computer or to another.
Both computer are 64bits, but different memory, internal HD, ...
Would it work? Is there any distribution that supports it?
Thanks

yes, I think that is possible, but you will/may have problems with the host specific configuration (like hostname, ip). It may depend on the setup and on what is installed and (how it was) configured.

Thanks for reply.

It's goin to be the same configuration. Host name, dhcp, ...
I've two computers, but I can't use always the same computer. If I install linux on external SSD and istall all software I like, I could star it in one computer or another.

#1 if the hardware is enough alike that should work.

#2 why not run one of a live-cd image from a thumb drive so you can have two machines running at the same time? Is there something very special about the OS install on this external drive?

Considering that the various "Live CD/DVD" distributions do this all the time, I'd say that your chances of success are pretty good as. The most likely stumbling block would be if the hardware were different enough that accessing your external drive required different drivers in the initrd. There are ways to include the needed modules for both in that initrd, so why not give it a try and see if it "just works", or if a little more effort is needed to get there.

Of course, this is all assuming that you would be choosing the same architecture (x86_64 vs. i386 vs. ARM, etc) for both machines.

GNU/Linux distributions are relatively hardware agnostic. Assumpted that you run a generic kernel (not stripped down and compiled for one type of hardware).
One other important thing is, that you have all other mounted filesystems (/home, /var... etc.) on the same boot disk.
I agree with the suggestion to run a live system from USB. If you have a small foorprint distro (Google is your friend) and enough RAM in both machines, you can run the system completely in RAM which is ridiculously fast. Tip to achieve this:
Set up a MX Linux 19 system (that is Debian Buster + some extra repositories).
Strip it down to the minimum you need (preferably with lightweight apps).
Use MX snalshot (pre-installed) to create a bootable ISO (called snapshot).
Put that on CD
Run the distro in "persistent mode" (read the docs).
Again: you need RAM...

Sorta sounds like ans SSD version of TAILS ?

Have you considered virtualization ? Install either virtualbox or KVM/libvirt on both computers and then keep the VM files on the external SSD. For virtualbox the 'machine folder' with the .vbox and .vdi files will be on the SSD. You can use symlinks so the VB installation on each computer points to a directory on the external SSD and a udev rule so that the SSD is always mounted to the same point on each host computer.

With virtualization you don't have to install an OS on two (or more) computers. You only have to run the same VM image. One of the major benefits of virtualization is easy migration from one host to another. In your case you would be alternating the host computer on which the VM runs.

One can easily test this with either the ssd drive or a large enough flash drive.

Thoughts.
You might have to adjust for the oldest machine. Most modern machines are still backward compatible.
The way it boots may need to be configured.
The video and network tend to be the most problem I'd wild guess.