We investigate collective spin-wave excitations and curvature-driven instabilities in concentrically arranged nanotubes coupled via antiferromagnetic interlayer exchange. By solving the linearized Landau–Lifshitz equation including exchange, anisotropy, interlayer exchange coupling, and nonlocal dipolar interactions, we show that curvature substantially reshapes the spin-wave spectrum and the spatial structure of the eigenmodes. As the number of nanotubes increases, the spectrum evolves into a multiband structure with hybridized collective branches and surface-localized modes. In contrast to planar multilayers, the tubular geometry breaks the equivalence between inner and outer boundaries, producing asymmetric surface localization, curvature-induced shifts of the nodal structure, and nonreciprocal spin-wave propagation. We further analyze magnetic instabilities through the softening of the lowest spin-wave modes. For weak radial anisotropy, a uniform mode governs the instability, whereas above a critical anisotropy the soft mode occurs at a finite wave vector, signaling an instability toward a stripelike modulation along the nanotube axis. Although curvature shifts the instability thresholds, the characteristic modulation period remains nearly independent of the tube radius. The overall dynamical behavior of the coupled nanotubes can be understood in terms of an effective curvature-induced anisotropy, which unifies the spectral reconstruction and instability thresholds. These results establish tubular multilayers as a platform in which geometry controls both collective spin-wave excitations and instability-driven magnetic phases.

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• Spin dynamics
• Nanotubes
• Synthetic antiferromagnetic multilayers
• Linear spin wave theory