Re4-xMnxGe7-δ (x = 0.9-1.5, δ = 0.42-0.44) is a new member of the Nowotny chimney-ladder family of compounds and features an incommensurate composite structure of transition element T (Re and Mn) and Ge substructures. Our theoretical calculations indicate metallic conductivity and ferromagnetic ordering, the latter being experimentally observed below 157 K.