Tm(3)Cu(4)Ge(4) crystallizes in the orthorhombic Gd(3)Cu(4)Ge(4)-type crystal structure (space group Immm) whereas Tm(3)Cu(4)Sn(4) crystallizes in a distorted variant of this structure (monoclinic space group C2/m). The compounds were studied by means of neutron diffraction, specific heat, electrical resistivity and magnetic measurements. Analysis of experimental data revealed the presence of an antiferromagnetic order below 2.8 K in both compounds. In Tm(3)Cu(4)Ge(4) the magnetic unit cell is doubled in respect to the crystal unit cell and the magnetic structure can be described by a propagation vector k = [0, 1/2, 0]. A larger magnetic unit cell was found in Tm(3)Cu(4)Sn(4), given by a propagation vector k = [1/2, 1/2, 0] (for simplicity the orthorhombic description is used for both the germanide and the stannide). Close to 2 K, in each compound an incommensurate antiferromagnetic order develops. This low-temperature magnetic phase is characterized by a propagation vector k = [1/4, 0, k(z)], where k(z) is close to 0.49 and 0.47 in Tm(3)Cu(4)Ge(4) and Tm(3)Cu(4)Sn(4), respectively. The antiferromagnetic phase transitions are clearly seen in the bulk magnetic and specific heat data of both compounds.