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We report on the static and dynamic magnetic properties of new family triangular lattice 2D magnets A2MnTeO6 (A=Na, Li, Ag, Tl). Specific heat and low-temperature neutron diffraction data reveal an onset of long-range magnetic order for all samples despite of the absence of any clear features on the magnetic susceptibility at low magnetic fields down to 2 K. The temperature dependence of magnetic susceptibility nicely follows the Curie-Weiss law in the high temperature range, but implies the wide range of the shortrange magnetic correlations and relatively large negative Weiss temperature, which suggests a predominance of antiferromagnetic exchange interactions and a noticeable spin frustration. In applied magnetic fields the temperature dependence of the magnetic susceptibility is remarkably changed and one can observe a characteristic maximum at Neel temperature. Additional confirmation of the magnetic field effect has been obtained from the ESR data, which clearly show the degradation and disappearance of the resonance signal at helium temperature. The behavior of ESR linewidth has been analyzed in terms of critical broadening and discussed.