Using extreme-ultraviolet (EUV) photometry obtained with the Extreme Ultraviolet Explorer (EUVE) satellite and UBVR optical photometry obtained with the 2.7 m telescope at McDonald Observatory, we have detected quasi-coherent oscillations (so-called dwarf nova oscillations) in the EUV and optical flux of the dwarf nova SS Cyg during its 1996 October outburst. There are two new results from these observations. First, we have for the first time observed frequency doubling: during the rising branch of the outburst, the period of the EUV oscillation was observed to jump from 6.59 to 2.91 s. Second, we have for the first time observed quasi-coherent oscillations simultaneously in the optical and EUV. We find that the period and phase of the oscillations are the same in the two wave bands, finally confirming the long-held assumption that the periods of the optical and EUV/soft X-ray oscillations of dwarf novae are equal. The UBV oscillations can be simply the Rayleigh-Jeans tail of the EUV oscillations if the boundary layer temperature kTbb 15 eV and hence the luminosity Lbb 1.2 × 1034(d/75 pc)2 ergs s-1 (comparable to that of the accretion disk). Otherwise, the lack of a phase delay between the EUV and optical oscillations requires that the optical reprocessing site lies within the inner third of the accretion disk. This is strikingly different from other cataclysmic variables, where much or all of the disk contributes to the optical oscillations.