  We classify constant mean curvature surfaces invariant by a 1-parameter group
of isometries in the Berger spheres and in the special linear group Sl(2, R).
In particular, all constant mean curvature spheres in those spaces are
described explicitly, proving that they are not always embedded. Besides new
examples of Delaunay-type surfaces are obtained. Finally the relation between
the area and volume of these spheres in the Berger spheres is studied, showing
that, in some cases, they are not solution to the isoperimetric problem.
