I am using eMClient 7.2.36908.0.
First I start a search resulting in several emails. The frirst one shows the full text on the right sight. 
When I select another mail, on the right side it shows only a headline, no full text.
After that any other mails text is not shown any more regardless if from the search or from any
other folder.
This does not happen with any search. I can easily recreate the problem with the same search,
but i could not find out any rule.
If you go to Menu > Tools > Accounts and click on the IMAP tab for this email account, then scroll down to the Offline section and select to download messages for offline use.
What I described is true for all local folders. If a mail on the list is opened by double klick, then the complete content is shown in a separate window. The problem is only in the preview area.
After a restart of eMClient everything is fine again until another search. But it only happens after some searches.
I was not able to reproduce this, sorry Gerhard.
Maybe download the installation file again from the Release History, and then uninstall eM Client making sure not to delete the database directory when prompted. Install from the new file and see if there is any difference.
Otherwise, if you have a Pro License, open a support ticket directly with eM Client.
Ok, I will try that later. For the next few days I have not much time. I’ll let you know about the result.
One question: After reinstall, do I have to redefine my accounts?
As long as you choose NOT to delete the database directory when asked, all your data and settings will still be there as before. That includes your messages, calendars, templates, account settings and passwords - everything. You just uninstall, download and install, and off you go. The 70MB download will probably take longer than anything else. 
I followed your procedure, but after new install there is no change. The problem is still there.
When showing the headline in the preview area, the just above the headline there are several little points running from left to right an the system seams to work hard.
Yes I have got a pro license and will open a support ticket.
Thank you!
That might be the best as they will be able to analyse your logs and determine where the problem is. Hopefully they find a solution.