Аннотация:The properties of acoustical double-negative media strongly depend on the frequency of a propagating wave. Particularly, the effective density and compressibility of a medium can be negative only at the certain frequency band. So it is very important to consider nonstationary processes in such media. The numerical simulations of the medium characterized by resonant-type density and compressibility response functions was performed in the article. It was based on the deduced matrix equation of a Lippmann-Shwinger type. The layer of “resonant” medium was placed inside an infinite background with constant density and compressibility. The incident impulse had a gauss form modulated by a certain carrier frequency. The effective density and compressibility of the layer change from both positive to both negative values while the impulse propagates through it. The phase velocity also becomes negative and the group velocity remains positive satisfying the causality principle. In the case of long enough impulse duration the layer behaves like it is made of a double-negative medium.