  We define a relative property A for a countable group with respect to a
finite family of subgroups. Many characterizations for relative property A are
given. In particular a relative bounded cohomological characterization shows
that if a group has property A relative to a family of subgroups, each of which
has property A, then the group has property A. This result leads to new classes
of groups that have property A. In particular, groups are of property A if they
act cocompactly on locally finite property A spaces of bounded geometry with at
least one stabilizer of property A. Specializing the definition of relative
property A, an analogue definition of relative amenability for discrete groups
are introduced and similar results are obtained.
