We have experimentally studied the collective spin-wave modes in microscopic magnetic structures formed by Permalloy disks, connected to each other by nanobridges. By using Brillouin light-scattering spectroscopy, we were able clearly to identify in-phase and out-of-phase modes and investigate their characteristics over wide intervals of the static magnetic field and the strength of the excitation signal. Our results show that the main characteristics of the modes are practically independent of the static field and the geometry of bridges, but are significantly affected by the nonlinearity.