Searches for pair production of squarks, sleptons, charginos and neutralinos are performed with the data collected by the ALEPH detector at LEP at centre-of-mass energies from 188.6 to 201.6 GeV. No evidence for any such signals is observed in a total integrated luminosity of about 410 pb−1. The negative results of the searches are translated into exclusion domains in the space of the relevant MSSM parameters, which improve significantly on the constraints set previously. Under the assumptions of gaugino and sfermion mass unification, these results allow a 95% C.L. lower limit of 37 GeV/c2 to be set on the mass of the lightest neutralino for any tanβ and sfermion mass. Additional constraints in the MSSM parameter space are derived from the negative results of ALEPH searches for Higgs bosons. The results are also interpreted in the framework of minimal supergravity.