On one space's page I have links to others space's pages, which is not accessble for all users, but the access have only some users, now if I haven'got access to this pages I see this links grey (not active), but I want to make it unvisible fot the users, who don't have permission to see it and to stay it visible only for some users, who have permission to see this pages. How can I make "grey" links to unvisible?
Out of the box, this is not possible.
You can have a look at the ServiceRocket Visibility plugin to see whether or not this provides you the functionality you are looking for.
This plugin is not available for Confluence OnDemand
You can also write a user macro (again, not for OnDemand) that could perform this functionality. You'd get the user object, check their permissions, and then conditionally show the content based on their permissions. There are several examples of doing similar things on this site.
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