Models describing systems of coevolving populations often have asympto
tically non-equilibrium dynamics (Red Queen dynamics (RQD)). We claim
that if evolution is much slower than ecological changes, RQD arises d
ue to either fast ecological processes, slow genetical processes, or t
o their interaction. The three corresponding generic types of RQD can
be studied using singular perturbation theory and have very different
properties and biological implications. We present simple examples of
ecological, genetical, and ecogenetical RQD and describe how they may
be recognized in natural populations. In particular, ecogenetical RQD
often involve alternations of long epochs with radically different dyn
amics.