What I am trying to do:
I have two identical rigs. I want to be able to pose each of the rigs and have that copied to the other rig.
Is that even possible?
I have already tried grouping… but it doesn’t seem linked posing is possible with that.
Bone constraints work, but only in one direction. I can pose the original rig, and have that copied to the duplicate… but there is no way to do the reverse.
Any ideas?
You can copy animation from rig1 to rig2:
Select rig1 (not animated), then SHIFT select rig2 (in object mode). CTR-L gives you the MakeLink menu. Choose ‘Animation Data’.
Now both rigs share the same animation data, which is what you might not want. Press U (Make Single User) and choose ‘Object Animation’. Now the two rigs’ animation data can be edited independently.
If you just want to copy over a pose from rig1 to rig2 and rig1 has a pose library, select rig2, enter pose mode and click on the icon next to the Pose Library title (in the Armature Data tab). This gives you a choice of the available Libs. Choose the according one.
Thank you for your response.
I guess I must be doing something wrong, because that doesn’t seem to do anything.
I selected rig1, shift-selected rig2, both in object mode. Both turn a nice bright shade of green. I linked the Animation Data, via CTRL-L.
What should happen now that they share the animation data? When I pose one rig, the other doesn’t change at all. Do the rigs have to be in a special format? Sharing names for the rig, for the bones? Hm… this is a lot deeper into Blender that I have been before. 
Copying poses would work, I guess… but I would like to pose both rigs in realtime. So that falls flat.
And another problem I stumbled over: I need the second rig to be mirrored. With a lot of fiddeling, I managed to get that working with bone constraints. But that means I still can pose only the original.
I guess this was just another of my completely crazy ideas that I cannot get to work in the way I imagined. 
Another method:
Change DopeSheet to ActionEditor: select rig2 and select the rig1’s “ActionToBeLinked”-button in order to select its Action.
Now rig 1 and rig 2 have the same animation data.
If this doesn’t work, the bones in the two Armatures might not have same names…?