  We investigate theoretically the interaction between integer and half-integer
Josephson vortices (fluxons and semifluxons) in an annular Josephson junction.
Semifluxons usually appear at the 0-$\pi$-boundary where there is a
$\pi$-discontinuity of the Josephson phase. We study the simplest, but the most
interesting case of one $\pi$-discontinuity in a loop, which can be created
only artificially. We show that measuring the current-voltage characteristic
after injection of an integer fluxon, one can determine the polarity of a
semifluxon. Depending on the relative polarity of fluxon and semifluxon the
static configuration may be stable or unstable, but in the dynamic state both
configurations are stable. We also calculate the depinning current of $N$
fluxons pinned by an arbitrary fractional vortex.
