  I predict the existence of internal spatial currents in a {\it single}
macroscopic quantum system, namely in trapped dilute-gas at sufficiently low
temperatures, when a Bose-Einstein condensation occurs. The spatial profiles of
the wavefunctions of low-lying states in such a system are different due to the
inhomogeneity, caused by an asymmetry of external trapping potential. This is
the reason for appearing of Josephson--like oscillations between atomic
subsystems in different states including the ground state as well. Using a
simple model for the wavefunctions of three low-lying states we demonstrate how
essential this effect can be. The possible applications of the predicted effect
are briefly discussed. Particularly, this effect opens the possibility to
identify experimentally the low lying excited states of a system.
