Thank you for your reply, but actually there is no any menu item "Selection and Outlining" in Blender as I know.
Properties(View) -> Scene -> Object selection(Default) -> Auto - Yes, it exist.
Would you be so kind to be more specific what did you do exactly?

A bit late…

Ok, I have found you attachments and also menu item.
So, this is here: Properties(View) -> Object -> Selection and Outlining -> Selectable.
It should be done for every object.
It wasn't in documentation(for normal object behaviour) and would be great to add it there.
Thank you.

Ok, I was wandering …

Full pass…

Step 1(Blender): http://ftp.nluug.nl/pub/graphics/blender/release/Blender2.76/blender-2.76b-linux-glibc211-x86_64.tar.bz2

Step 2(Blend4web SDK): https://www.blend4web.com/pub/blend4web_sdk_free_15_12.zip

Step 3(Getting Started With the Blend4Web SDK (with subtitles) ): https://www.youtube.com/watch?v=RAC8i5nvSg4

Step 4: Made simple project(attached with exported html from Blender, you can test json by "Fast preview").

Step 5(Project mechanics):
5 objects exist: torus, cube, sphere, cylinder, cone.
Cylinder, cone - invisible from start. - Work!
Select tor - move camera on start point. - Work!
Select cube - hide: torus, cube, sphere; show - cylinder; move camera on start point. - Work!
Select sphere - hide: torus, cube, sphere; show - cone; move camera on start point. - Work!
Select cylinder - hide: cylinder; show - torus, cube, sphere; move camera on start point. - Doesn't Work!
Select sphere - hide: cone; show - torus, cube, sphere; move camera on start point. - Work!

Interesting…

Hi,
could anyone tell me where to start,
if project which was exported works with logic nodes in json but doesn't in html?