The propagation of electrostatic surface modes on a thin dusty plasma slab has been investigated in different dust fugacity regimes. For wave frequencies much smaller than the grain charging frequency and for long wavelengths, it is shown that dusty plasmas support three different types of surface modes, namely, the dust–acoustic surface wave (DASW), the dust charge–density surface wave (DCDSW) and the dust–Coulomb surface wave (DCSW) which exist, respectively, in the low fugacity (tenuous), medium fugacity (dilute) and high fugacity (dense) regimes. In the short wavelength range, there exists a new kind of surface mode called “dusty plasma surface wave” (DPSW) which has no counterparts in the volume modes. This new mode exists over a wide range of dusty fugacity (from tenuous to dense regime). On the other hand, for frequencies much larger than the grain charging frequency, the DASWs exist also in the dilute regime, while the DCSWs are found to be absent. In the short wavelength limit, the DPSWs continue to exist even in the high-frequency range. Explicit dispersion relations as well as the damping rates due to the grain charge fluctuations are derived in each case. The results obtained for the various surface modes are compared with those for the case of volume modes.