A probabilistic seismic hazard analysis is applied to the sites of the main cities (Chania, Rethymno and Heraklion) of Crete island, Greece, to compute probabilities of exceedance of specified values of peak ground acceleration (PGA) and to estimate maximum possible PGA at each site. The methodology allows the use of historical or instrumental data, or a combination of both. The instrumental part of the data can be divided into subcatalogues with each having an individual minimum threshold magnitude for completeness. Also incorporated into the procedure were recently published maximum possible magnitudes for each site (6.48, 5.21, 7.52 for Chania, Rethymno and Heraklion, respectively) and an attenuation law for shallow seismicity in Greece [ln(PGA) = 3.52 + 0.70Mw- 1.14 ln(R2+h20)1/2+ 0.12S+/- 0.70], where R and h0 are, respectively, the epicentral distance and focal depth in kilometres, S is 0, 1 or 2 depending on soil conditions and PGA is in units of cm s-2. The maximum PGA for Heraklion varies from 0.130g (S= 0, rock) to 0.165g (S= 2, soft). All three sites are coastal, and alluvium is the dominant soil type, for which S= 2. Probabilities that a given PGA will be exceeded at least once during time intervals of 1, 5, 25 and 50 yr were also computed. Additionally, maximum PGA values associated with `design earthquakes' were computed. For earthquakes at epicentral distances of 10 +/- 5 km, median values of maximum PGA were 0.23g, 0.09g and 0.42g at Chania, Rethymno and Heraklion, respectively.