Аннотация:The decisive role of magnetic anisotropy even in systems with small or nearly negligible anisotropy is illustrated for the layered antiferromagnets MnSb2O6 and Na3Ni2SbO6. While the magnetic phase diagrams of both compounds have been studied by static magnetisation, specific heat, and thermal expansion studies up to 15 T, low-energy magnon modes enabling precise quantitative determination of magnetic anisotropy have been investigated by high-frequency/high field electron spin resonance. Both systems show long range antiferromagnetically ordered ground states. In Na3Ni2SbO6, there is a tricritical point at TN = 16.5 K which separates two distinct antiferromagnetic phases from the paramagnetic regime. The phase boundaries are visible in the dynamic response of the antiferromagnetic (AFM) resonance modes, too. The anisotropy gap Δ = 360 GHz implies considerable uniaxial anisotropy. The data suggest a crucial role of axial anisotropy favoring the AF1 spin structure over the AF2 one. In contrast, in MnSb2O6 we observe AFM resonance modes with a zero-field splitting of Δ = 20 GHz which imply very small planar anisotropy. Again, a crucial role of the anisotropy is suggested by competing antiferromagnetic phases appearing, at T = 2 K, in small magnetic fields. We conclude the importance of the anisotropy favoring the cycloidal ground state at B = 0 T