The magnetic ordering of the novel binary compounds Dy3Ge4 and DyGe1.3(1) has been studied by neutron diffraction and magnetic measurements. Dy3Ge4 with the Er3Ge4 structure type (space group Cmcm) displays a two step antiferromagnetic ordering below TN = 19 K. The two Dy sites (Dy1:8(f) and Dy2:4(c)) order independently with two distinct order parameters associated with the same wave vector q = (0, 1, 0). Both sublattices have a uniaxial antiferromagnetic moment arrangement but with mutually perpendicular orientations. Dy1 orders below TN with the moments along the a-axis, Dy2 orders only below Ti = 6 K along the c-axis. At 1.4 K the moment values of Dy1 and Dy2 are 7.31(8) μB and 5.6(3) μB, respectively. Their arrangement leads to a symmetry reduction described by the monoclinic magnetic space group Cp1121′/mi′(Sh1155). The two-dimensional canted antiferromagnetic structure is the result of a strong magnetocrystalline anisotropy and the presence of various types of magnetic interactions. The phase of DyGe1.3(1) composition with the AlB2 structure type (space group P6/mmm) was detected as an impurity in the studied sample. It orders antiferromagnetically below TN = 16 K with collinear moment arrangement associated with a 2c-cell enlargement (q = 0, 0, 1/2) described by the magnetic space group P2c112′/m′(Sh1156). At 1.4 K μDy = 7.2(2) μB and is confined to the (001) plane.