PACS 71.20.Mq, 71.20.Ps Most ab-initio calculations of the electronic structure use the local density approximation, which gives good structural data but severely under-estimates the band gaps of semiconductors and insulators. This paper presents calculations of the band structures of some important oxide semiconductors and insulators, using the screened exchange method and the weighted density approximation, which give improved band gaps. The methods are tested on diamond, Si, Ge, MgO, Al 2 O 3 , and SiO 2 and the main interest is for