  A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is
derived variationally from Hamilton's Action Principle using microscopic
conservation of mass, and macroscopic conservation of total magnetic helicity,
cross helicity and entropy, as the only constraints on variations of density,
pressure, fluid velocity, and magnetic vector potential over a relaxation
domain. A novel phase-space version of the MHD Lagrangian is derived, which
gives Euler--Lagrange equations consistent with previous work on exact ideal
and relaxed MHD equilibria with flow, but generalizes the relaxation concept
from statics to dynamics. The application of the new dynamical formalism is
illustrated for short-wavelength linear waves, and the interface connection
conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of
whether $\vec{E} + \vec{u}\times\vec{B} = 0$ should be a constraint is
discussed.
