  We study the minimal dimension of the classifying space of the family of
virtually cyclic subgroups of a discrete group. We give a complete answer for
instance if the group is virtually poly-Z, word-hyperbolic or countable locally
virtually cyclic. We give examples of groups for which the difference of the
minimal dimensions of the classifying spaces of virtually cyclic and of finite
subgroups is -1, 0 and 1, and show in many cases that no other values can
occur.
