  In this paper we discuss the two-sided limit shadowing property for
continuous flows defined in compact metric spaces. We analyze some of the
results known for the case of homeomorphisms in the case of continuous flows
and observe that some differences appear in this scenario. We prove that the
suspension flow of a homeomorphism satisfying the two-sided limit shadowing
property also satisfies it. This gives a lot of examples of flows satisfying
this property, however it enlighten an important difference between the case of
flows and homeomorphisms: there are flows satisfying the two-sided limit
shadowing property that are not topologically mixing, while homeomorphisms
satifying the two-sided limit shadowing property satisfy even the specification
property. There are no homeomorphisms on the circle satisfying the two-sided
limit shadowing property but we exhibit examples of flows on the circle
satisfying it. It can happen that a suspension flow has the two-sided limit
shadowing property but the base homeomorphism does not, though it is proved
that it must satisfy a strictly weaker property called two-sided limit
shadowing with a gap (as in \cite{CK}). We define a similar notion of two-sided
limit shadowing with a gap for flows and prove that these notions are actually
equivalent in the case of flows. Finally, we prove that singular suspension
flows (in the sense of Komuro \cite{K}) do not satisfy the two-sided limit
shadowing property.
