Compatible nonlocal Poisson brackets of hydrodynamic type, and   integrable hierarchies related to them
  In the present work, the integrable bi-Hamiltonian hierarchies related to compatible nonlocal Poisson brackets of hydrodynamic type are effectively constructed. For achieving this aim, first of all, the problem on the canonical form of a special type for compatible nonlocal Poisson brackets of hydrodynamic type is solved. 
O. I. Mokhov