Searches for scalar top and scalar bottom quarks have been performed at center-of-mass energies between 161 GeV and 183 GeV using the L3 detector at LEP. No signal is observed. Model-independent limits on production cross sections are determined for the two decay channels <math><mtext>t</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub></math>→c<math><mtext>χ</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub><msup><mi></mi><mn>0</mn></msup></math> and <math><mtext>b</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub></math>→b<math><mtext>χ</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub><msup><mi></mi><mn>0</mn></msup></math>. Within the framework of the Minimal Supersymmetric extension of the Standard Model mass limits are derived. For mass differences between <math><mtext>t</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub></math> and <math><mtext>χ</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub><msup><mi></mi><mn>0</mn></msup></math> greater than 10 GeV a 95% C.L. limit of 81.5 GeV is set on the mass of the Supersymmetric partner of the left-handed top. A supersymmetric partner of the left-handed bottom with a mass below 80 GeV is excluded at 95% C.L. if the mass difference between <math><mtext>b</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub></math> and <math><mtext>χ</mtext><mtext>̃</mtext><msub><mi></mi><mn>1</mn></msub><msup><mi></mi><mn>0</mn></msup></math> is greater than 20 GeV.Facultad de Ciencias Exactas