The quasi-two-dimensional antiferromagnet CsDy(MoO4)2 is studied by neutron diffraction and quasielastic neutron scattering. The crystal structure of two low-temperature phases (below 120 K and below 40 K) is determined. An approximate structure of the magnetically ordered phase (<$E T sub N ~=~1,36~roman K>) is proposed. In the ordered state the order-parameter critical exponent <$E beta~=~0,17(0,01)>, the in-plane correlation length exponent <$E nu~=~0,94(0,07)>, and the staggered susceptibility critical index <$E gamma~=~1,01(0,04)> were determined. Comparing these results to the exact solution for a 2D Ising magnet we conclude that, although 2D behavior is apparent in CsDy(MoO4)2, there are deviations from the simple 2D Ising model.

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