The magnetic structure of EuCu2Ge2 has been determined by flat-plate neutron powder diffraction. Two magnetic phases are present in the neutron diffraction pattern at 3.5 K. They have the same moment, within error, and a common transition temperature. Both 151Eu and 153Eu Mössbauer spectroscopy show that the two magnetic phases belong to the same crystallographic phase. Both phases can be modelled by planar helimagnetic structures: one with a propagation vector of [0.654(1), 0, 0], the other with a propagation vector of [0.410(1), 0.225(1), 0].