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- → qq̄g̃g̃ and qq̄q̃q processes. Stable squark pair production, and stop pair production with subsequent decays into a stable gluino, t̃ → cg̃, 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) GeV/c2, and stable hadronizing gluinos are excluded up to 26.9 GeV/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 GeV/c2 is set on the stop quark mass.