  Hamiltonian structures for non-linear hydrodynamics of incommensurate
intergrowth compounds (IIC) and quasicrystals (IQ) are constructed. We discuss
also the way to account for internal friction of phason nature. We show that
the existence of a self-force in IIC and IQ is not only matter of constitutive
issues, rather it is related with questions of SO(3) invariance. The covariant
mechanics of discontinuity surfaces in quasiperiodic structures is also
analyzed. The attention is mainly focused on the interaction between `diffuse'
grain boundaries and sharp discontinuity (moving possibly) surfaces.
