Could it simple be the return address in the account set-up is the Gmail address?

Thanks Paul...I have looked at Gmail and all appears ok....it is driving me nuts!

When you say you've looked at Gmail, do you mean you looked at the settings in Google or the settings in Thunderbird? I meant the latter.

In the left-hand pane in Thunderbird click on the top level folder for the account. This brings up a screen in the main pane with headings Email, Accounts and Advanced features. Under Accounts, select View Settings for this account. That should show what the reply to address is set to for this account. There could also be a set of identities for this account, each with their own reply address. There's a Manage Identities button at the bottom right. (I've got this set up for my main account as I use several e-mail addresses with one account.)

Even if the reply address is blank (which I would guess means it uses the main e-mail address as the reply address) you could set the reply address to what you want it to be.

There could be a remote possibility that your correspondents are using an old e-mail address notwithstanding what you've set up as your reply address because they think they know better. Unlikely, but I recently received an e-mail from my brother (not a reply) that was sent to a version of my e-mail address that I haven't used for about 20 years.

Paul, I totally appreciate your assistance with this issue....ok, I have checked the reply address for each email account I have in Thunderbox and found all three to contain my yahoo address, the one I wish to use. Despite this your reply, under my yahoo name arrived in my gmail account, as well as my yahoo account! Other emails are arriving in my yahoo account but are going directly to the Trash box?? Paul.

Of course, my replies are not going to any reply address you may have set up in Thunderbird, but are sent via the Mozilla support website, so I'd guess in this case they are going to whatever address you've set up when you registered for Mozilla support. As a point of reference, the reply to address for the e-mail I just received notifying my of your update to the question is no-reply@mozilla.org.

Beyond that,, I'm out of ideas.

Ok, well many thanks anyway...it seems I still have work to do:....the emails that have arrived correctly to my yahoo inbox have mysteriously disappeared the next time I opened Thunderbox....I am unable to locate them anywhere....I don't know how to disable the show only 'unread' messages.

I suggest you log into the gmail account at gmail.com and remove the setting you have to pick up mail from yahoo. The settings are probably here https://mail.google.com/mail/u/0/#settings/accounts

Conversely you may have set yahoo to forward to gmail, but I think that the first option is what is happening. When Google pick up the mail, they delete it at yahoo and hence it disappears from your IMAP mail account in Thunderbird.

Thanks Matt...I'll check all that.

Thanks to all who have responded to my posting....it appears that I did have some contradictory settings in Yahoo, Gmail and Thunderbox. My Yahoo emails were being intercepted by Gmail and deleted, Thunderbox was understandably confused.... it seems my simplest solution being to remove the connection with Gmail and simply manually check for Gmail emails occasionally.

Paul