  Recent discovery of mesoscopic electronic structures, in particular the
carbon nanotubes, made necessary an investigation of what effect may helical
symmetry of the conductor (metal or semiconductor) have on the persistent
current oscillations. We investigate persistent currents in helical structures
which are non-decaying in time, not requiring a voltage bias, dissipationless
stationary flow of electrons in a normal-metallic or semiconducting cylinder or
circular wire of mesoscopic dimension. In the presence of magnetic flux along
the toroidal structure, helical symmetry couples circular and longitudinal
currents to each other. Our calculations suggest that circular persistent
currents in these structures have two components with periods $\Phi_0$ and
$\Phi_0/s$ ($s$ is an integer specific to any geometry). However, resultant
circular persistent current oscillations have $\Phi_0$ period.
\pacs{PACS:}PACS:73.23.-b
