constant. A similar limitation exists for any insulator-layered superconductor boundary, if the dielectric constant ε$_{ext}$ of the insulator is less than ε . The above conditions follow from the dispersion relation for the JPWs and the natural limitation for the tangential component q ( q = k sin θ < k, k = ω/c ) of the wave-vector for a wave incident at an angle θ from the vacuum onto the layered superconductor. A simple analysis shows that the above inequality is compatible with the dispersion relation for JPWs only for frequencies ω$_{J}$ < ω < ω vac 1 . In other words, any wave with frequency ω > ω vac 1 incident from the vacuum cannot propagate further in a layered superconductor. JPWs with ω > ω vac 1 can only match evanescent waves in the vacuum. As for frequencies ω$_{J}$ < ω < ω vac 1 , the NRI can be observed, but only for incident angles θ higher than some critical value θ$_{crit}$ . For frequencies in the interval we predict the existence of a new branch of surface waves (here γ = λ$_{c}$/λ$_{ab}$ ≫ 1 is the current-anisotropy parameter, λ$_{c}$ = c/ω$_{J}$ε 1 / 2 and λ$_{ab}$ are the magnetic-field penetration depths along and across the layers, respectively). Despite numerous works on this issue, SJPWs with frequencies higher than ω$_{J}$ were not discussed before. Here we study them and prove that the SJPWs spectrum consists of two branches. The low-frequency branch was described in detail in [6]. Its spectrum ω ( q ) follows the “vacuum light line”, q = ω/c , and deviates from it at frequencies close to ω$_{J}$ . The new branch of SJPWs predicted here starts at the frequency ω = ω vac 1 and follows the vacuum light line for ω ≪ ω$_{2}$ . For frequencies of the order of ω$_{2}$ , the dispersion curve ω ( q ) strongly deviates from the vacuum light line and stops at the frequency ω = ω$_{2}$ when q ≈ 1 /λ$_{ab}$ . Thus, SJPWs do not exist within the frequency gap ω$_{J}$ < ω < ω vac 1 . On the other hand, as shown here, this is actually the range where the NRI can be observed (for waves incident from the vacuum onto the layered-superconductor boundary). Hence, some kind of complementarity between the NRI and surface waves is established in this paper. Conditions for the observation of NRI .— Consider a layered structure consisting of su- perconducting and dielectric layers with thicknesses s and d , respectively (see Fig. 1). We study the transverse-magnetic JPWs propagating with wave-vector k$_{s}$ = ( q, 0 , κ $_{s}$) and hav- ing the electric, E s = { E s $_{x}$, 0 , E s z } , and magnetic, H s = { 0 , H $^{s}$, 0 } , components proportional to exp[ i ( qx + κ $_{s}$z − ωt )]. The coordinate system is shown in Fig. 1. 3 ω vac 1 < ω < ω$_{2}$, ω$_{2}$ = ω$_{J}$γ, (1)