A comprehensive study of the magnetic phase transitions in Tb 3 Co has been undertaken combining different techniques. Using single crystal neutron diffraction in the paramagnetic state a weak crystal structure distortion from the room temperature orthorhombic structure of the Fe 3 C type described with the Pnma space group toward structure with lower symmetry has been observed with cooling below 100 K. At 81 K there is a second order phase transition to an antiferromagnetic incommensurate phase with the propagation vector k = (0.155, 0, 0). As derived from thermal diffusivity measurements, the critical exponents for this transition are very close to the 3D-Heisenberg universality class, proving that the magnetic interactions are short-range but with a deviation from perfect isotropy due to crystal field effects. At T 2 70 K there is another magnetic phase transition to a ferromagnetic state whose character is shown to be weakly first order. The low temperature magnetic state has a non-coplanar ferromagnetic structure with strong ferromagnetic components of Tb magnetic moments along the crystallographic c-axis. The application of an external magnetic field B = 2 T along the