In this paper the computational properties of mesomorphic media, intermediate between quantum atomic-molecular structures and continuous macrophysical media, are discussed. It is shown that the mesomorphic media make it possible to realize noninertial high accuracy linear and nonlinear adders, perform Lebesgue integration operations and solve almost all high- and ultrahigh dimension and complexity algebraic problems by direct methods without loss of stability. The problems of the equilibrium and nonequilibrium dynamics and control of dynamic objects with local and distributed properties can be solved using this approach. Hardware implementation of the computational properties of the mesomorphic media is discussed.