  The generic magnetic phase diagram of multiferroic RMn$_2$O$_5$ (with R=Y,
Ho, Tb, Er, Tm), which allows different sequences of ordered magnetic
structures for different R's and different control parameters, is described
using order parameters which explicitly incorporate the magnetic symmetry. A
phenomenological magneto-electric coupling is used to explain why some of these
magnetic phases are also ferroelectric. Several new experiments, which can test
this theory, are proposed.
