We demonstrate some general characteristics of time-delayed reacting hydrodynamical (TDRH) systems. Time-delayed reactions in a local system cause the de-stabilization of the steady state of reactions and make the system approach nonlinear limiting trajectories, some of which were not seen in non-delayed systems. The necessary magnitude of delayed-time τ for the de-stabilization is, for the cases where there are only delayed reactions, at most a fourth of the period of the oscillation around the steady state. Hence hydrodynamical coupling between these local systems always exhibits an instability in small scales which eventually leads to a blow-up because whatever small the non-zero time-delay τ is, it is sufficient for the de-stabilizations of very short-period, i.e. small-wavelength, sound waves.