Invasive species are a leading cause of the current biodiversity decline, and hence examining the major traits favouring invasion is a key and long-standing goal of invasion biology. Despite the prominent role of the advertisement calls in sexual selection and reproduction, very little attention has been paid to the features of acoustic communication of invasive species in nonindigenous habitats and their potential impacts on native species. Here we compare for the first time the transmission efficiency of the advertisement calls of native and invasive species, searching for competitive advantages for acoustic communication and reproduction of introduced taxa, and providing insights into competing hypotheses in evolutionary divergence of acoustic signals: acoustic adaptation vs. morphological constraints. Using sound propagation experiments, we measured the attenuation rates of pure tones (0.2-5 kHz) and playback calls (Lithobates catesbeianus and Pelophylax perezi) across four distances (1, 2, 4, and 8 m) and over two substrates (water and soil) in seven Iberian localities. All factors considered (signal type, distance, substrate, and locality) affected transmission efficiency of acoustic signals, which was maximized with lower frequency sounds, shorter distances, and over water surface. Despite being broadcast in nonindigenous habitats, the advertisement calls of invasive L. catesbeianus were propagated more efficiently than those of the native species, in both aquatic and terrestrial substrates, and in most of the study sites. This implies absence of optimal relationship between native environments and propagation of acoustic signals in anurans, in contrast to what predicted by the acoustic adaptation hypothesis, and it might render these vertebrates particularly vulnerable to intrusion of invasive species producing low frequency signals, such as L. catesbeianus. Our findings suggest that mechanisms optimizing sound transmission in native habitat can play a less significant role than other selective forces or biological constraints in evolutionary design of anuran acoustic signals.