Searches for stable, hadronizing scalar quarks and gluinos are performed using the data collected with the ALEPH detector at LEP. Gluon splitting into a gluino or a squark pair is searched for at centre-of-mass energies around the Z resonance, in the e + e- →\ensuremathqq¯\ensuremathg~\ensuremathg~ and \ensuremathqq¯\ensuremathq~q~¯ processes. Stable squark pair production, and stop pair production with subsequent decays into a stable gluino, \ensurematht~→c\ensuremathg~ , are also directly searched for at centre-of-mass energies from 183 to 209 GeV. Altogether, stable hadronizing stop (sbottom) quarks are excluded up to masses of 95 (92) \ensuremathGeV/c2 , and stable hadronizing gluinos are excluded up to 26.9 \ensuremathGeV/c2 , at 95% confidence level. In the framework of R-parity-conserving supersymmetric models in which the gluino and the stop quark are the two lightest supersymmetric particles, a 95% C.L. lower limit of 80 \ensuremathGeV/c2 is set on the stop quark mass.