Searches for a scalar top quark and a scalar bottom quark have been performed using a total data sample of 56.8 pb −1−1 at a centre-of-mass energy of s√=s= 183 GeV collected with the OPAL detector at LEP. No candidate events were observed. Combining this result with those obtained at lower centre-of-mass energies, the 95% C.L. lower limit on the scalar top quark mass is 85.0 GeV if the mixing angle between the supersymmetric partners of the left- and right-handed states of the top quark is zero. The lower limit is 81.3 GeV, even if the scalar top quark decouples from the Z0Z0 boson. These limits were obtained assuming that the scalar top quark decays into a charm quark and the lightest neutralino, and that the mass difference between the scalar top quark and the lightest neutralino is larger than 10 GeV. The complementary decay mode of the scalar top quark in which it decays into a bottom quark, a charged lepton and a scalar neutrino was also studied. From a similar analysis, a mass limit on the light scalar bottom quark was set at 82.7 GeV for a mass difference between the scalar bottom quark and the lightest neutralino larger than 7 GeV, and at 84.0 GeV for the mass difference larger 10 GeV and the lightest neutralino heavier than 30 GeV. These limits were obtained assuming that the scalar bottom quark decays into a bottom quark and the lightest neutralino, and that a mixing angle between the supersymmetric partners of the left- and right-handed states of the bottom quark is zero.