Abstract
Common fixed point results for families of single-valued nonexpansive or quasi-nonexpansive mappings and multivalued upper semicontinuous, almost lower semicontinuous or nonexpansive mappings are proved either in CAT(0) spaces or
R
-trees. It is also shown that the fixed point set of quasi-nonexpansive self-mapping of a nonempty closed convex subset of a CAT(0) space is always nonempty closed and convex.