The historical development of the effort to define the physical units objectively is described. The beginning of this effort is situated to the end of XVIII. Century. The first coherent system of units based by C.F. Gauss, is mentioned, together with the next development using this method, finished by introduction of SI system. The essence of article is dealing with the tendencies to base the units definitions on the fundamental physical constants or natural invariants, such as Planck constant, elementary charge, speed of light an others. The negative influence of the new definition of amper - applying the Josephson and the quantum Hall effect - on the coherency of SI system is described. The aim to introduce a new definition of mass unit - to abolish the prototype of kilogram and to define it on the base of fundamental constants – is described, together with the connected problems.