  We find a fine structure in the Aharonov-Bohm effect, characterized by the
appearence of a new type of periodic oscillations having smaller fractional
period and an amplitude, which may compare with the amplitude of the
conventional Aharonov-Bohm effect. Specifically, at low density or strong
coupling on a Hubbard ring can coexist along with the conventional Aaronov-Bohm
oscillations with the period equal to an integer, measured in units of the
elementary flux quantum, two additional oscillations with periods $1/N$ and
$M/N$. The integers $N$ and $M$ are the particles number and the number of
down-spin particles, respectively. {}From a solution of the Bethe ansatz
equations for $N$ electrons located on a ring in a magnetic field we show that
the fine structure is due to electron-electron and Zeeman interactions. Our
results are valid in the dilute density limit and for an arbitrary value of the
Hubbard repulsion $U$
