During the flag raising ceremony at the Yuri Dologorukiy submarine, the first in the Project 955 class, Commander of the Russian Navy reported that the Navy "paid special attention to the torpedo armament [of the new submarine] and its capability to carry long-range cruise missiles." That is, of course, in addition to the 16 Bulava ballistic missiles that will be deployed on Project 955 submarines.
The cruise missile in question is most likely the 3M10/RK-55 Granat or maybe a newer missile, Kalibr (which was recently tested in a launch from the Severodvinsk Project 885 attack submarine). The missiles can be launched from one of the eight standard 533-mm torpedo tubes deployed on Project 955 boats. A submarine of this class is reported to carry up to 40 weapons that could use torpedo tubes, but these would include torpedoes and anti-ship missiles as well as long-range SLCMs. These cruise missiles, of course, can carry nuclear warheads, although at this point there is no reason to believe that they will.
Setting aside the question why would a strategic missile submarine need long-range SLCMs on board, this is an interesting development that brings back the discussion of whether Russia counts long-range SLCMs as strategic delivery vehicles and therefore whether it believes they should be covered by the 1992 pledge to remove all tactical nuclear weapons from its surface ships and submarines.
I looked into this issue some time ago and I believe that my main conclusion still stands - Russia did remove all nuclear SLCMs from its submarines and reported zero deployed missiles in its annual declarations. I would still argue that in doing so Russia effectively accepted that long-range SLCMs are non-strategic systems, but I admit that it is not a very strong argument. As long as the START reporting arrangement was in place, it provided an enforcement mechanism of sorts, but it expired with the START treaty in December 2009, so nothing prevents Russia from asserting its position that long-range nuclear SLCMs are not covered by the 1992 pledge. There is a proposal to resume the START SLCM data exchange, but I don't see why Russia would agree to do that. More likely, it will prefer to maintain ambiguity and to leave its options open.
Any discussion of further nuclear reductions would have to deal with SLCM anyway, so it's not something that would derail the process (not that it needs help with that). But the gray status of nuclear SLCMs as systems that are not covered by New START but at the same time not really non-strategic would definitely complicate things.