One-dimensional lattice with the nearest neighbour interaction is considered. If the interaction is harmonic, the system has its counterpart or the “dual” in which the mass of each particle is replaced by a force constant, the force constant by a mass and certain conditions are imposed. The systems thus defined behave the same and have the same frequency spectra. The concept of the dual systems is not restricted to those with harmonic forces. As an example, equivalence of a special anharmonic chain and a semi-relativistic chain is shown.