In some categories when I go to then second page of category.
1. I press the link of page 2.
2. My url become www.lux4man.ru/katalog/aksessuary_dlya_k...galki/?limitstart=48

But I still remain on the first page, and i see the list of products of the first page.

When I go page 3
My url become
www.lux4man.ru/katalog/aksessuary_dlya_k...galki/?limitstart=96
And I see the list of products og the page 3.

And the secon page becomes unavalable

Why could this happen?

It happens in this category
www.lux4man.ru/katalog/aksessuary_dlya_kureniya/zazhigalki/
and some others

Screenshot:
screencast.com/t/KtvRr7iv

Hi,
Thank you for the example. That's really a strange behavior.
Find the katalog/aksessuary_dlya_kureniya/zazhigalki SEF URL in JoomSEF's URLs manager and post its associated Real non-SEF URL. Are there any duplicate SEF URLs stored for it?
Do you use some custom rewrite rule in your .htaccess file that could cause this?

Hi!

Here is the link:
screencast.com/t/ot6zJvR5Mx

No duplicates:
screencast.com/t/yT0rV5DYTHa6

Here is
.htaccess
Nothing special
screencast.com/t/ggbHRcRxy9
screencast.com/t/A4uDrgo1DN5

Everything looks all right on your screenshots.
But what's strange is, that when I first tested it yesterday, page 3 didn't work for me, but you said that page 2 didn't work for you. When I test it again today, all pages are working fine for me in the category.
Which leads me to thinking that there was maybe just some problem with cache in Joomla or JoomSEF.