  A general appearance of two-pole structures is exhibited in a relativistic
Friedrichs-Lee model combined with a relativistic quark pair creation model in
a consistent manner. This kind of two-pole structure could be found when a
$q\bar q$ state couples to the open-flavor continuum state in the $S$ partial
wave. We found that many enigmatic states, such as $f_0(500)/\sigma$,
$K_0^*(700)/\kappa$, $a_0(980)$, $f_0(980)$, $D_0^*(2300)$, $D_{s0}^*(2317)$,
and $X(3872)$, together with another higher state for each, all result from
this kind of two-pole structures. Furthermore, an interesting observation is
that this kind of two-pole structure will contribute roughly a total of
180$^\circ$ phase shift for the scattering process in a single channel
approximation. This relativistic scheme may provide more insights into the
understanding of the properties of non-$q\bar q$ state. It is also suggested
that such two-pole structure could be a common phenomenon which deserves
studying both from theoretical and experimental perspectives.
