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 qbar{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-qbar{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.