The atomic structures of two important metastable phases that coexist with beta' in the Al-Mg-Si system have been solved. U1 has a trigonal unit cell with a=b=4.05Å, c=6.74Å. It contains five atoms in the space group P-3m1 (164), with composition MgAl2Si2. U2 is orthorhombic having unit cell parameters a=6.75,Å, b=4.05Å and c=7.94Å. It consists of twelve atoms packed in the space group Pnma (62) with composition Mg4Al4Si4. Initial models were extracted by analysing electron nano-diffraction (NDP) data. Refinements by ab initio quantum mechanical electron diffraction using a multi slice least square (MSLS) method converged to very similar results. The intensities of the simulated diffraction patterns fit the experiment with overall R-values below 5%.