I am am slowly figuring about what is happening.

Probably you have had enabled basic SEF in Joomla before installation if JomSEF. Then your basic URLs have been rewritten by Joomla to some new URLs. You have probably used this new URLs as internal links.

When you have installed JomSEF, your basic URLs have been rewritten to another new URLs (different from old SEF). JomSef understands only basic URLs, but do not understand old SEF URLs .... actually all old SEF URLs are broken links!

Am I right? I would appreciate opinion of some JomSEF support expert about this issue.

I am lucky that I did not have a lot internal links. So, I have disabled manually. However, I have another much bigger website and I am sure that I will not use JomSEF there. It would generate too much broken links.

Hello zmauko,

yes you are perfectly right. That could be very likely the reason.
Well, one note, you shoud always use the original non-sef version of the URLs even in articles (that is index.php?option=...). There is plugin called System SEF, that will turn then to correct links - if you have just Joomla SEO on then to Joomla SEO compatible links, when JoomSEF is on then to JoomSEF links.

Plus note that JoomSEF is able to redirect all these old style URLs to new ones using 301. (check the configuration - Advanced tab, Redirect old to new ones)