katya wrote: How I can permit an auto publication comments for registered users only.
But if user not registered comments is to be moderated!
Just using K2 and not some other extension, your question interested me so I checked the Paramaters button when in K2 itself. It allows you to allow commenting by everyone and to either auto publish or not. So, if you wanted unregistered to auto publish, you have to set auto publish on. However, you cannot have everyone set to allow comments but only registered auto publish in the straight forward K2.
There may be an extension you can find to allow that either here, through Joomla extensions or through a Google search (not all extensions are listed here or at Joomla extensions) but if you cannot find one, you are going to have to hire a programmer to do it for you. The only alternative is set auto publish on and restrict to registered or you WILL attract idiots.
Greg.