Searches for a scalar top quark and a scalar bottom quack have been perform
ed using a data sample of 182 pb-l at a centre-of-mass energy of root s = 1
89 GeV collected with the OPAL detector at LEP. No evidence for a signal wa
s found. The 95% confidence level (C.L.) lower limit on the scalar top quar
k mass is 90.3 GeV if the mixing angle between the supersymmetric partners
of the left- and right-handed st;states of the top quark is zero. In the wo
rst case, when the scalar top quark decouples from the Z(0) boson, the lowe
r limit is 87.2 GeV. These limits were obtained assuming that the scalar to
p quark decays into a charm quark and the lightest neutralino, and that the
mass difference between the scalar top quark and the lightest neutralino i
s larger than 10 GeV. The complementary decay mode of the scalar top quark
decaying into a bottom quark, a charged lepton and a scalar neutrino has al
so been studied. From a search for the scalar bottom quark, a mass limit of
88.6 GeV was obtained if the mass difference between the scalar bottom qua
rk and the lightest neutralino is larger than 7 GeV. These limits significa
ntly improve the previous OPAL limits. (C) 1999 Elsevier Science B.V. All r
ights reserved.