The main question studied in this article is how the preference of MgO for six- or fivefold bonding in rocksalt or h-MgO structures, respectively, affects the local bond lengths near Mg atoms in wurtzite structured MgxZn1-xO alloys. A first-principles study of MgxZn1-xO alloys has been carried out in the range 0 < x < 0.5 to determine the local wurtzite parameter u, axial bond lengths, and the band gaps. Disorder in the alloys is simulated using the special quasirandom structure approach. The authors found that axial Mg-O bond lengths are longer than the axial Zn-O bond lengths for all possible concentrations, but the u values are still far away from the h-MgO value of 0.5. The band gap is found to increase linearly with Mg content. They found no signs of transformation to the lower energy h-MgO structure until x is about 50%.