A search for pair-production of long-lived, heavy, singly-charged particles has been performed with data collected by the ALEPH detector at a centre-of-mass energy of 172 GeV. Data at are also included to improve the sensitivity to lower masses. No candidate is found in the data. A model-independent 95% confidence level upper limit on the production cross section at 172 GeV of 0.2–0.4 pb is derived for masses between 45 and 86 GeV/c2. This cross section limit implies, assuming the MSSM, a lower limit of 67 (69) GeV/c2 on the mass of right- (left-) handed long-lived scalar taus or scalar muons and of 86 GeV/c2 on the mass of long-lived charginos.