At least I found the solution, even though it's not very good:
1) Copy relative SEF link from the frontend
2) Find 2 variants of it in JoomSEF URL Manager
3) Find URL responsible for the default layout, untick 'Active'
4) (!)Strange thing, but then the blog layout becomes inactive, so click one more time
5) Do this for each menu item which isn't displayed correctly

Maybe the problem is about confusing default and blog layouts by JoomSEF.

Have you set the "Add layout to URL" option to "Always" or "Only when different from default"? In that case, there shouldn't be the same SEF URL for both layouts. Of course you need to delete the URLs first and clear the cache, so the URLs get recreated with the new settings.
As regards the Active column - if there's more than one same SEF URLs, the one you click in the Active column becomes active, which means that one will always be used, otherwise the URL to be used will be selected depending on some priorities (article has higher priority than category etc.).

david wrote:

My site has already got some age, I can't do that.
But at least the problem has been solved, everything is working OK and I can have some rest:).
Thank you for the help, David, best regards to you and your group.
Yuriy.