You can export them to a file on one machine and import them from that file on the other machine.

in the Address Book on the first machine:

1. Select an address book (e.g. Personal Address Book).
2. Go to Tools|Export
3. Select a file in which to store the chosen address book. Given that you're moving from one Thunderbird to another, the LDIF option is most useful. Give this file a distinctive name, different from the address book's original name. (e.g., I use pab.ldif for "Personal Address Book", ca.ldif for "Collected Addresses".)
4. Repeat for each address book that you want to transfer.

Save your new files to a USB stick or similar. Plug this into your second machine.

In the Address Book on the second machine:

1. Go to Tools|Import.
2. Select Address Book.
3. Select Text.
4. Navigate to your USB stick and select one of your exported address book files.
5. Import it.
6. Repeat for each address book you exported.

Note that it will create a new address book for each imported file, each one taking the name of the file it came from. You can now select all the Contacts in a new address book (use ctrl+a) and drag them to a preferred address book.

Hello Zenos,

Thank you very much for your answer. This saves me a lot of time because typing all my emailaddresses over again would have been a lot of work. I'm very happy with your help, thanks!!!

I wish you a nice day! With kindly regards,

Helga.