The structure and conformations of 1,2-dimethoxycyclobutene-3,4-dione in the vapor at a temperature of 185 degrees C have been measured by gas-phase electron diffraction. The molecule exists in two forms, one of symmetry C-2v with the methyl groups trans to the double bond, and one of C-s symmetry with a methyl group cis and the other trans to this bond (these forms hereafter designated as trans and cis). The molar ratio trans/cis is 68/32 with a 2 sigma uncertainty of about 24. Many of the parameter values for the two forms are very nearly alike and could not be measured experimentally. With the adoption of parameter differences calculated at the B3LYP/cc-pVTZ level, the following bond distances (r(g)/angstrom) and bond angles (angle/deg) with estimated 2 sigma uncertainties were obtained for trans/cis: C1=C2 = 1.381(9)/1.381, C1-C4 = 1.493(11)/1.495, C3-C4 = 1.543(20)/1.545, C-O = 1.203(4)/< 1.200 >, C1-O = 1.316(6)/< 1.320 >, O-CH3 = 1.444(9)/< 1.443 >, C-C-C3 = 93.1(5)/< 93.1 >, C3-C4-O = 136.7(29)/< 136.9 >, C-C-O = 131.0(23)/137.5, and 131.8, C-O-C = 117.2(12)/118.2 and 116.9; the individual angle values for the cis form listed as averages differ very little. The bond distances and bond angles are in excellent qualitative agreement with prediction based on conventional ideas about the effects of conjugation and hybridization, and their relative values agree very well with predictions from quantum mechanical calculations.