Searches for scalar top and bottom quarks have been performed with data collected by the ALEPH detector at LEP. The data sample consists of 21.7 pb - 1 taken at s = 161, 170, and 172 GeV and 5.7 pb - 1 taken at s = 130 and 136 GeV. No evidence for scalar top quarks or scalar bottom quarks was found in the channels t → cχ, t → bl, and b → bχ. For the channel t → c χ a limit of 67 GeV/c 2 has been set on the scalar top quark mass, independent of the mixing angle between the supersymmetric partners of the left and right-handed states of the top quark. This limit assumes a mass difference between the t and the χ of at least 10 GeV/c 2 . For the channel t → bl the mixing-angle independent scalar top limit is 70 GeV/c 2 , assuming a mass difference between the t and the of at least 10 GeV/c 2 . For the channel b → b χ, a limit of 73 GeV/c 2 has been set on the mass of the supersymmetric partner of the left-handed state of the bottom quark. This limit is valid if the mass difference between the b and the χ is at least 10 GeV/c 2 .