Spin waves in a two-dimensional planar magnet are considered in the temperature range below the transition point. The resonance line determined by the magnetic susceptibility has an unusual shape. The resonance frequency is the branch point of the susceptibility of the order of 2Δ - 1, where Δ is the scaling dimensionality of magnetization. The singularity indicated can be displayed in the line shape of ferromagnetic resonance or in inelastic neutron scattering. The effects of a weak external field, an anisotropy, and an interaction between layers in layered systems are discussed.