In recent years it has been established that the natural mineral polymorphs atacamite and clinoatacamite (chemical formula Cu2Cl(OH)3) exhibit a low temperature magnetic behavior characteristic for frustrated magnetic systems. Over the years, attempts have been undertaken to establish the ordered ground state magnetic structures of the two compounds, which for various reasons however appear inconclusive from a present perspective. Therefore, we propose to study the magnetic structures of single crystalline atacamite and clinoatacamite by means of elastic neutron scattering, this way for the first time addressing this issue for the first material, and readdressing it for the second material by utilizing an improved sample quality.