  The persistent current for a one-dimensional ring with two tunnel barriers is
considered in the limit of weakly interacting electrons. In addition to a small
off-resonance current, there are two kinds of resonant behavior; (i) a current
independent of the barrier transparency (true resonance) and (ii) a current
analogous to the one for a ring with only a single barrier
(``semi''-resonance). For a given barrier transparency one or the other type of
resonant behavior is realized depending on a geometric factor (ratio of
interbarrier distance to ring circumference) and on the strength of the
electron-electron interaction. It is shown that a repulsive interaction favours
the``semi''-resonance behavior. For a small barrier transparency the
``semi''-resonance peaks are easily washed out by temperature whereas the true
resonance peaks survive.
